# Aptitude - Alligation or Mixture - Discussion

### Discussion :: Alligation or Mixture - General Questions (Q.No.1)

1.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

[A].
 1 3
[B].
 1 4
[C].
 1 5
[D].
 1 7

Explanation:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

 Quantity of water in new mixture = 3 - 3x + x litres 8

 Quantity of syrup in new mixture = 5 - 5x litres 8

 3 - 3x + x = 5 - 5x 8 8

5x + 24 = 40 - 5x

10x = 16

 x = 8 . 5

 So, part of the mixture replaced = 8 x 1 = 1 . 5 8 5

 Sandhya said: (Jul 16, 2010) Can you give a shortcut for this?

 Kiran said: (Jul 29, 2010) As there are 3 parts of water and 5 parts of syrup. total upto 8 parts.In terms of percentage,syrup is 60% and water is 40%.So syrup content to be reduced to 10% and water content to be increased to 10%,total constitutes to 10%+10%=20%. finally 20%=20/100=1/5

 Murali said: (Sep 9, 2010) I did not get last Step. Could you please explain how it was? So, part of the mixture replaced = (8/5) * (1/8) =1/5.

 Surendrareddy said: (Sep 10, 2010) NOTE: Liquid = Mixed substance (water,syrup) Let the volume of the vessel = x liters. Out of this x liters 3/8(x) is water & 5/8(x) is syrup. Let y liters of liquid is taken out. So out of this y liters 3/8(y) is water and 5/8(y) is syrup. The water in the remaining liquid is 3/8(x-y) . The syrup in the remaining liquid is 5/8(x-y). Now y liters of water is added to the remaining liquid so that the final liquid contains half water and half syrup. => 3/8(x-y)+y=5/8(x-y) =>y=1/5(x) or y = 1/5(x). Answer: The amount of liquid drawn out = The amount of water added = 1/5 of x.

 Vigneshwaran K said: (Sep 29, 2010) Hai I can't understand the steps can you please give me the understandable steps. Thank you.

 Nitesh said: (Oct 7, 2010) @ Surendrareddy. You are rocking. This is the right way.

 Uma said: (Oct 15, 2010) I am agree with Siri. Your way of explanation is also excellent. Thanks.

 Amuthan said: (Oct 16, 2010) Great work Surendara Reddy.

 Bindhureddy said: (Oct 28, 2010) @surendrareddy. Your way of explanation is good. Moreover it is easy to do.

 Krishan said: (Dec 9, 2010) @Surender reddy. its nice approach to solve it thanks..

 Krishjlk@Gmail.Com said: (Dec 15, 2010) Your great surender. Thanks a lot. Really that is very good explanation. Instead of remembering the formulas you came with the theory. And concept. Good excellent. Thank you for your post.

 Mahi said: (Dec 22, 2010) How we will get 60% of syrup from 5 parts of syrup and 40% of water from 3 parts of water which is explained in Kiran's answer?. Please explain in detail. Please.

 Vikas said: (Dec 26, 2010) Yes mahi, something wrong with Kiran's answer. 3/8= 37.5% 5/8= 62.5% And its not 40% and 60% as told by kiran

 Kalyan said: (Feb 2, 2011) @Mahi and Kiran Since it is 3 parts and 5 parts...totally 8. 50% of 8 is 4 and 40% of 8 is 3. So 60% of 8 is 5 parts. Hope you understand.

 Uttam said: (Feb 5, 2011) Let X=volume of vessel Y=volume of mix taken out. Initially, volume of water in vessel=3X/8 volume of syrup in vessel=5X/8 Y=volume of mix taken out=volume of water added. Now, drawn off mix may contain, volume of water=3Y/8. volume of syrup=5Y/8. after mix drawn off, volume of water in the vessel=(3X/8)-(3Y/8)=(3/8)(X-Y). volume of syrup in the vessel=(5X/8)-(5Y/8)=(5/8)(X-Y). After water added, volume of water in the vessel =[(3X/8)-(3Y/8)]+Y =[(3/8)(X-Y)]+Y. hence from the Question,in the vessel, volume of water =volume of syrup [(3/8)(X-Y)]+Y=(5/8)(X-Y) 10Y=2X Y=(1/5)*X So volume of water should be added is (1/5)th of volume of vessel.

 Megha said: (Feb 11, 2011) Thanks it is really a good way to solve it.

 Ravi said: (Mar 1, 2011) Uttam and surender. Your answer is perfect. Kiran is wrong.

 Ameer said: (May 6, 2011) Thank you Surender and Utham...i hav tried to explain the answer in detail Let the volume of vessel be x quantity of water = 3/8 x quantity of syrup = 5/8 x Let the amount of mixture removed be y The removed mixture contains 3/8 y of water and 5/8 y of syrup So quantity of water left in the mixture=3/8[x-y] quantity of syrup left in the mixture 5/8 [x-y] According to the question,the amount of mixture removed is replaced later by water,so that the syrup an water would be exactly half each of the mixture... so when more water is added to the existing water in the mixture.. 3/8[x-y] + y = 5/8[x-y] 3x/8 - 3y/8 +y = 5x/8 - 5y/8 y = 2x/8 - 2y/8 8y=2[x-y] 4y=x-y x=5y y=1/5 x

 Ramakhanna said: (May 15, 2011) Thanks ameer for your detailed explanation...

 Manasa said: (Jun 10, 2011) Uttam, surender and ameer has cleared out my confusion regarding this problem. Thanks a lot.

 Victor said: (Jun 24, 2011) Simple solution for this; Given: Vessel contains...water -- 3 parts. Syrup -- 5 parts. Required: Both should be half-- half Sol: take one part of syrup and add it to water i.e then both will have 4 parts. So divide syrup into 5 parts.then one part is 1/5, that is the solution.

 Chacha Chodhary said: (Jun 25, 2011) Here is simple approach 3/5-1/2=1:1

 Surya said: (Jul 1, 2011) Can you solve this problem with allegation formula ?

 Supreeth said: (Aug 31, 2011) Victor your way of doing this problem is less time consumable. Thank you.

 Hari said: (Sep 7, 2011) As kiran said about getting the percentage. How its possible, can you explain it clealy of getting 60%, 40 %.

 Preethi said: (Sep 14, 2011) Excellant victor.

 Divya said: (Sep 20, 2011) Thanks victor. Your way of explanation is short and simple.

 Sunny said: (Sep 22, 2011) Good victor.

 Satyam said: (Oct 5, 2011) Thank you kiran.

 Vipin Kumar said: (Nov 3, 2011) Water contains 3 parts and Syrup contains 5 parts, so total there are 8 parts there in the vessel. now as asked , that in final mixture both water and syrup should be present half-half i.e 4 parts of water and 4 parts of syrup. water syrup initial- l3 5 final- 4 4 so, final amount=initial amount(1-amount tobe replaced/total amount) Note: here u should take syrup's amount not water.(If the question would be, to replace the mixture with syrup then take water's amount. 4=5(1-K/8), K=8/5 Most questions u can solve by this , but i did not get how they got 1/5 as an answer.

 Prateek said: (Dec 1, 2011) Why is that nthey got 1/5 only becoz syrup is considered? w s 3 5 +1 -1 4 4 So 1/5 is correct, right? why not 1/3?

 Mayank said: (Jan 3, 2012) 40% of 8 parts is 3.2 and 60% is 4.8 how it's possible to get them as 3 and 5 as this is a big difference .

 Nisha said: (Jan 7, 2012) I think amir done good solution.

 Varsha said: (Jan 18, 2012) Thanks ameer.

 Vaishali said: (Jan 22, 2012) I am getting 8/5 as the amount to be replaced. If there is 8litres of the total liquid then 3 litres is water and 5 litres is syrup. Now suppose if you remove x litres of the liquid the remaining liquid is 8-x. In this 8-x, 3/8(8-x) is water and 5/8(8-x) is syrup. Now if we add x litres of water to it the equation we get is 3/8(8-x)+x=5/8(8-x) since both the syrup and the liquid equals 4/8 Solving this equation we get x=8/5 Where did 1/5 come from? Please somebody explain. I am highly confused.

 Yogi said: (Feb 3, 2012) The first one itself is short solution. as we assume total soln as 8litre so if x litre of water is added by replacing So net water remains is 3-3x/8+x in 8 litre and syrup is 5-5x/8 equalize both as both becomes equal in content aftr previous replacement. we get x=8/5 but this is replecement if we assume cotent of vessel =8l so part of replcement=replced amount/total amount this means (8/5)/8 = 1/5 ans

 Sam said: (Feb 22, 2012) Great surendra reddy.

 Kamini Jain said: (Apr 12, 2012) I did not get it why 8/5 is multiplied with 1/8.

 Baljeet said: (Apr 29, 2012) Good victor.

 Vky said: (Jun 3, 2012) Here x=8/5 is the amount in liters that has been added to make up 8 liters in total. This added quantity constitutes some part of the total volume. Right? So, this some part is stated as (x/8). Hope everyone's doubt on this has been cleared. => (8/ (5*8) ) =1/5. 1/5th is the part (not liters) from the total 8liters that has been added. Thank You.

 Chinmayi said: (Jun 8, 2012) Formula for this type of question:. (1/2) (difference in parts/greater part).

 Ami said: (Sep 1, 2012) Suppose initial quantity of mixture is 1 lit. ratio water:syrup = 3:5,so syrup is 3/8 alligation method 3/8 1(pure water so taken as 1) 1/2 1/2 1/8 qt of mixture 1/2 -------------= --- qt of water 1/8 1-x/x=4,so x=1/5 (x= quatity of water removed or qt. of syrup withdraw)

 Susmitha said: (Oct 3, 2012) Here given 8 parts of total, 3 parts water &5 parts syrup. Then we equal the both water & syrup ratio. Now we add the 1 part of syrup from 5 parts of syrup i.e;1/5 then it will become equal parts of water & syrup. The answer is:1/5.

 Kousik Maji said: (Feb 9, 2013) Here total mixture is(3+5)=8. Now syrup=5/8 and water=3/8. If we take some mixture and added same amount of water then amount of syrup will be 1/2 and water 1/2. Now the amount of syrup present in removed mixture is 5/8-1/2=1/8. Now 5/8 syrup present in mixture 1. 1/8 ........................(8/5)X(1/8)=1/5.

 N.Anusha said: (Mar 9, 2013) Thanks @Kousik Maji for your good solution but I am confused with bellow sentence please give clear cut info. 1/8 ........................(8/5)X(1/8)=1/5.

 Mathkamsutra said: (Apr 30, 2013) @Kiran how you got 60% and 40% If I do - (3/8)*100 it gives 37.5%, How you got 60 and 40?

 Guru said: (May 25, 2013) I think the issue with some of the guys here is they find these mathematical theories hard to understand. Let me make it simpler for them. They didn't give the volume of vessel in the question so never mind that. The vessel contains 8 parts of liquids (i.e. - 3 parts of water and 5 parts of syrup). What they are asking is to make the mixture into half water and half syrup i.e. - 4 parts of water and 4 parts of syrup. To make it happen you need to take 1 part of syrup out of the vessel (which is 1/5th of the total syrup) and add 1 part of water instead and thus you get the answer 1/5!

 Sybil said: (Jun 19, 2013) A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20% litres of the first solution to make a solution of 10% sugar?

 Tapan Kumar Raul said: (Jun 21, 2013) It is a common sense. Finally in the solution 50% syrup & 50% water will remain. That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter. => 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.

 Radheshyam said: (Aug 19, 2013) Let volume is 8. Water = 3/8 syrup = 5/8. According to question, Suppose y mixture(water,syrup)are drawn. Water quantity is 3y/8 and syrup quantity is 5y/8. 3/8-3y/8+y = 5/8-5y/8. y = 1/5.

 Abhidhamm said: (Sep 17, 2013) Ratio given is 3:5 (AS 3 Part water & 5 part syrup). Take even LCM of 3 & 5 i.e. 24, 30 etc. Suppose we take 24 as LCM. Now divide LCM by 8 (addition of ratios i.e. 3+5). So, 24/8=3. Now, multiply both the terms of ratio by 3. So we get 9 (water) and 15 (syrup). As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12. So we get 3/15= 1/5.

 Viswavikram said: (Sep 20, 2013) Can we able to solve this problem in alligation method, if so explain?

 Akshara said: (Sep 23, 2013) How would you taken 1/8 as a part of mixture in the last step? could you please explain?

 Rahul Wiley said: (Nov 2, 2013) Hey Keep it simple. Fraction of syrup in final Mixture = (Fraction of syrup in initial mixture)*(1 - x/v). Where, x is the Quantity of mixture removed. V is the volume of the Mixture.

 Rajesh said: (Dec 15, 2013) Simple friends, Here totally 8 parts (5 part syrup + 3 part water). To make it equal (4 parts syrup + 4 part water). So, we have to draw 1 part from syrup (i.e.,) 1/5.

 Usha said: (Feb 3, 2014) How we get 5x+24=40-5x?

 K.S Pal said: (Mar 30, 2014) A container is filed with 3 part water & 5 parts syrup, so total we have 8 parts or mathematically we can say, 3/8 water. 5/8 syrup. Suppose we withdraw x parts of mixture then this will contain, 3/8(x) water. 5/8(x) syrup. Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically. 3/8-3/8(x) +x = 5/8-5/8(x). It will give x = 1/5.

 Jerry said: (Apr 26, 2014) Why do we add y in this step 3/8[x-y] + y = 5/8[x-y] ? The rest of the steps are perfectly understood! Thanks :),.

 Mohan said: (May 28, 2014) Hey guys I think this is useful formula for this question: 1/2(difference in parts/greater part). 1/2(5-3/5). 1/5.

 Anonymous said: (Jun 17, 2014) From where did you get 1/8 in finding the final result?

 Yogita said: (Jun 29, 2014) How we find the % of thing?

 Vaishali Sharma said: (Jul 9, 2014) There has to be a direct formula for this. Anyone has it?

 Prabha Prabcuteatgmaildotcom said: (Jul 16, 2014) Mean litre, m = (l+s)/2. m = 4. Proportion x = (l-m)/l. x = 5-4/5. x = 1/5. Pure and Simple.

 Mohi said: (Jul 20, 2014) I cannot understand. Its so difficult for me. Please explain in another way.

 Harleen said: (Jul 30, 2014) Let there be 8 liters of solution, in which 3/8 liter be water and 5/8 lt be syrup. As we can see syrup is more than water so of course some syrup is to be replaced with water. As it is a solution and we can't remove only syrup or water so we have to remove the whole solution and replace it with water. Now using ratio and proportion (5-(5x/8))/(3-(3x/8)+x) = 1/1. As some part of syrup will be removed we also have to remove water as i have told that we are replacing some part of whole solution with water thats why we are subtracting 5x/8, 3x/8 from numerator and denominator respectively, now after removing solution we have add equal quantity of water thats why we will add water in denominator which will be equivalent to the quantity of the solution removed i.e 5x/8+3x/8=x. On the RHS side value will be as we want both the syrup and water in same proportion i.e 1/1.

 Rohit Thakur said: (Aug 3, 2014) 1. Let volume of vessel be x. Now the ratio is 3:5 initially. (3/8)x water and (5/8)x syrup. 2. Now let y liter of mixture drawn off. Means now {(3/8)x - (3/8)y} water and {(5/8)x - (5/8)y} syrup in remaining mixture. 3. Now y liters of water mix to make the equal quantity of both water and syrup, Then, 3/8(x-y)+y = 5/8(x-y), y = 1/5x.

 Jamuna said: (Aug 5, 2014) What is the another way to solve this problem even more easier?

 Minisha said: (Oct 10, 2014) Can anyone solve this equation for me? 3-3x/8+x = 5-5x/8

 Manish said: (Dec 2, 2014) Let there be 1kg of mixture with water concentration 3/8 i.e. 3/8 kg water present. X kg mixture is removed so water removed = 3X/8. Now X kg pure water is added. In the required mixture water = 1/2 kg. So balancing over water. 3/8 " 3X/8 + X = 1/2 solving we get X = 1/5.

 Amar said: (Dec 13, 2014) Easy solution : 3 parts + 5 parts = 8 parts. For equality (3+1) parts + (5-1) parts = 4 parts (equals). Hence we need to reduce 1 part that will be from 5 parts. Hence : 1 (part)/5(parts) is reduced. Hope you understand.

 Ankita said: (Jan 29, 2015) Can anybody gives the easiest way of solving it?

 Aatish said: (Apr 23, 2015) Concentration = a(1 - y/x)^n. Remaining Syrup/Total volume = Concentration. a = contamination of original solution, here in this case is 3:5 Viz 3/8. Since water is 3 parts and syrup is 5 part that means the solution is contaminated with 37.5% in terms of syrup. Now, Concentration = 1/2 (since, 50 % solution is desired). Therefore, Using the above formula, 1/2 = 3/8(1 - y/x). Here y = quantity of mixture drawn off. x = initial volume. We don't know either so leave it as it is. Solving we get, Y/x = 1/4. Now, Y:x::1:4. Therefore, y = 1/1+4 = 1/5. i.e 1 part of solution has been drawn off for per 5 part of the solution.

 Ankita said: (May 3, 2015) How is the equation solved? i.e. How do we get, 5x+24? Can anybody explain?

 Sadik Shaik said: (May 11, 2015) To make equal parts, we just take 1 part from syrup and replace with water to get 4 parts of water and 4 parts of syrup. So we are replacing 1 part of syrup of 5 parts with water, so the answer is 1/5.

 Anand Shaw said: (May 11, 2015) Water in one mixture : 3/8. Water in another mixture : 1. Water in new mixture : 1/2. According allegation formula: Ratio of quantity of two mixtures mixed : (3/8-1/2) : (1-1/2) = 4:1. So 1/5 parts of another mixture is mixed with one. Another mixture is pure and is same as mixture replaced.

 Rakesh Jha said: (May 14, 2015) @Anand shaw. Your method is good. But last passage after 4:1 can you elaborate more?

 Prakash.M said: (May 28, 2015) I don't understand none of the method above said. Can anyone tell mathematically?

 Dinesh said: (Jun 3, 2015) Before going to shortcuts I explain some known facts about this question. 1. Only water is added and no effect on syrup. 2. So think like how much water is added so that mixture is 1:1. Lets start my shortcuts: Water:Syrup 3:5. After mixing water 1:1. We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5. Finally we see: Before 3:5. After 5:5. Clearly we see that two part of water is added. Hence amount of water added as new solution is gives answer. 2/10 = 1/5. Trick is based on how much you think and how much you understand.

 Dinesh said: (Jun 3, 2015) Before going to shortcuts I explain some known facts about this question. 1. Only water is added and no effect on syrup. 2. So think like how much water is added so that mixture is 1:1. Lets start my shortcuts: Water:Syrup 3:5. After mixing water 1:1. We know syrup has no loss and no gain so we first make part of syrup is 5. Hence we multiply by 5 in 1:1, we get 5:5. Finally we see: Before 3:5. After 5:5. Clearly we see that two part of water is added. Hence amount of water added as new solution is gives answer. 2/10 = 1/5. Trick is based on how much you think and how much you understand.

 Ashwin said: (Jun 18, 2015) Hey @Kiran I didn't understand you. How you get 60% and 40%?

 Preeti Rani Dass said: (Jun 20, 2015) Can you explain with the other method?

 Venugopal said: (Jun 29, 2015) @Victor. Why did you divide syrup into 5 parts?

 Subhankar said: (Jun 30, 2015) (bigger - smaller)/(2xbigger).

 Ricky said: (Jul 17, 2015) The liquid still remains in 3:5 even after drawing off some liquid. Now to bring it into 1:1 we will have to add 2 to 3 I mean just 40% of remaining syrup. Now if after drawing off some liquid, the quantity of the solution is 8 litres i.e.3 litres water and 5 litres syrup we have to add 2 litres water to bring it in 1 : 1 which means 2 litres of 10 litres were removed. Which is 2/10 or 1/5 or 20%.

 Vijay said: (Sep 26, 2015) Let 3x+5x = 24.....(1). 8x = 24. x = 3 substitute in (1). Then water is 9 and syrup is 15. To make both equal subtract 3 from syrup and add it to water. So, 3/15 = 1/5.

 Vcillusion said: (Oct 19, 2015) For 62.5% water, to get to 50%, 12.5 must go which is exactly 20% of 62.5. Syrup is to water = 3 : 5. % water in mixture = 5/8*100 = 62.5%. Desired % of water = 1/2*100 = 50%. Difference = 62.5-50 = 12.5%. To get 50% of water the 12.5% must go. Hence Formula = Difference/Current Water in Mixture. = 12.5/62.5 = 1/5 = 20 %. 5 syrup parts of 8 = 62.5% syrup, to get to 50%, 12.5 must go which is exactly 20% of 62.5.

 Viuay said: (Nov 2, 2015) I totally can't understand please explain in easiest way.

 Vivek said: (Nov 5, 2015) Let be x liters of mixture. From equation quantity of pure liquid = x*(1-y/x)^n. Where why is quantity of water used. N is no. of times water replaces the liquid. x liters of mixture and why liters of water final quantity of pure liquid = 1/2*x. So from equation 1/2*x = 5/8*x(1-y/x). Where 5/8*x is the initial quantity of syrup. We need to find out y/x. So, 1/2 = 5/8*(1- y/x). 1-(y/x) = 4/5. y/x = 1-(4/5). y/x = 1/5.

 Ramakrishna said: (Dec 1, 2015) @Chacha chodary. I did not get can you explain clearly?

 Ram said: (Jan 12, 2016) What if ratios are 2:1:2?

 Vish said: (Jan 12, 2016) Quantity of syrup = x(1-y/x) raise to n, n = 2. Here, 8(1-3/5) raise go 2. = 4/5. So quantity of water = 1-4/5 = 1/5.

 Vinod said: (Feb 4, 2016) Water : Syrup. 3:5. Water = 3x. Syrup = 5x. Volume = 8x. Why liters mixture withdrawn and replaced with water. Applying the condition. 3x-3/8y+y = 5x-5/8y. 16x = 10y. 8x = 5y. y = 8x/5. y = Volume/5.

 Neeru said: (Feb 6, 2016) I think density of both ingredient is of some importance. That can be further related to concentration.

 Jitendra said: (Mar 27, 2016) Let the volume of the mixture be 8 litres, in which 3 litre is water and 5 litres is syrup. Now add 2 litre of water in the mixture, the volume becomes 10 litre and the ratio becomes 1:1. Since the earlier mixture was 8 litre in volume. Therefore we have to subtract 2 litres from the new mixture, so as it becomes 8 litres. Now calculate how much part of the mixture was subtracted from the new mixture i.e. (2/10 or 1/5).

 Raj said: (Apr 14, 2016) Actually the correct answer is 8/5.

 Vishal said: (Apr 19, 2016) For 8 litre ---> full 1 part. So, 8/5 litre --->?

 Bala said: (May 6, 2016) Hi, Can anyone clear my doubt? How do they get this step? Quantity of water in new mixture = 3 -((3x/8)+ x) litres.

 Sandeep said: (May 7, 2016) Anyone, please clear my doubt. How (3 - 3x / 8 + x) = 5x + 24?

 Jomson Joy said: (Jul 1, 2016) Thanks, vicllusion. It is the simple method.

 Sundar said: (Jul 5, 2016) You guys all great. Knowing how to solve a problem in an easy way is great and explaining to others is a bigger than that. Great helping kind. Once again Thank you all.

 Prakash said: (Jul 12, 2016) Please, anyone solve it in alligation formula.

 Rajnish Jha said: (Jul 27, 2016) New quantity of syrup = 5x - 5y. New quantity of water = 3x - 3y + 8y = 3x + 5y. They are equal to each other. => 5x - 5y = 3x + 5y. => 2x = 10y. => y/x = 2/10 = 1/5. => 8y/8x = 1/5.

 Anurag Srivastava said: (Aug 2, 2016) Let us assume there is total 80 liter of mixture I take 80 for easy division of water and syrup you can take any number or x. So mixture contains 3 part water and 5 part syrup mean there is total 8 part. 8 part is 80. So 1 part will be 80/8 = 10 litre. Water is 3 part=30 litre. Syrup is 5 part=50 litre. Let why litre of syrup is taken out and replace with water for an equal proportion of water and syrup. Then the quantity of water = quantity of syrup. 30 + y = 50 - y. By solving y =10 litre this quantity is taken out form syrup 50 litre. So this is how many parts of syrup. It is 10/50 = 1/5 part since the answer is in part according to question 1/5th part of syrup should take out and replace by water. You can solve accordingly above with x litre instead of 80litre but x can confuse so always take numerical value for easy calculation. Thanks, I hope it is understandable.

 C.H.Udhay said: (Aug 4, 2016) Superb @Kiran.

 Disha said: (Aug 7, 2016) How came 5x + 24 = 40 - 5x?

 Muni said: (Aug 13, 2016) Hi. People who didn't understand why the answer is 1/5 and not 8/5. It's because of twist in question. They asked what part of the total mixture. 3 part water + 5 part liquid = 8. Assume 8 liter is the total mixture. We got 8/5 liter now see what 8/5 liter percentage in 8 liters. Ie (8/5) / 8. = 8/5 * 1/8. = 1/5. Trick is in question. So in options they didn't mention units because its a const. Thank you.

 Abd said: (Aug 23, 2016) 8/5 * 1/8 is done because part of the mixture has to be replaced. Since a part of the mixture is 1/8, the final answer is multiplied with it.

 Anirudh said: (Sep 2, 2016) Hi, To make this easier to understand, let us conduct a balance of all the things involved in this problem. Consider A to be the initial amount of liquid in a vessel which contains 3 parts water and 5 parts syrup. Let B be the amount of this liquid to be removed and C be the amount of water to be added to get "D" amount of liquid that has 50% water and syrup. Writing it in the form of an equation, We have A + C = B + D. From the question, we can see that the amount of liquid = amount of water added. Hence C = B, A = D. Now assuming the vessel to contain 1 liter of liquid, by conducting an input/output balance for water, we have: (3/5 + 3)%A + (100)%C = (3/5 + 3)%B + (50%)D, [100% because it is pure water] As A is 1 liter and A = D and B = C, We have (0.375 x 1) + C = 0.375 x C + (0.5 x 1), C = 0.2 litre or 1/5 liter. Hope this will helpful for all.

 Iram said: (Sep 7, 2016) Attention to those who want to understand the solution provided with the question. Suppose the vessel initially contains 8 litres of liquid. ------> vessel contains => 8l mixture. Let x litres of this liquid be replaced with water. Quantity of water in new mixture = 3 - (3x/8) + x litres. ------ >[3lit water it originally contained] - [ (3x/8) l water which was removed when you removed 'x' l mixture] + ['x' litre water that you added]. Hope that'll justify the remaining solution too.

 Haniffa said: (Sep 22, 2016) WATER : SYRUP 3 : 5 = 8. 2 : 0 = 2 (TO BOTH BECOME EQUAL ADD 2 UNITS TO WATER). 5 : 5 = 10 (RATIO IS EQUAL NOW). SO, ADDED AMOUNT OF WATER IS 2/10 OF FULL AMOUNT. IF YOU SIMPLIFIED IT'S 1/5.

 Silpa said: (Oct 3, 2016) Assume we have 80 liters of the solution. Then, we will be having 30 liters of water and 50 liters of syrup. Let x be the % of water that we have to add to the solution, to increase the % of water to 50%. 30 + x/80 + x = 1/2. => x = 20.

 G.Muniyandi said: (Oct 24, 2016) Let water be 0.6 L whereas syrup is 1L. 0.6 + 0.2 = 0.8 : 1 - 0.2 = 0.8 1 : 1, 0.2/1=1/5. (Here, to solve the problem without complex one thing is to have it in our mind that is what amount of water is taken from a mixture which is filled with the same amount of water again. Thus how much amount of syrup is drawn off from the mixture that is taken in our consideration then 0.2/1 = 1/5 is answer.

 Santhosh Ravvala said: (Oct 27, 2016) Nice explanation @Victor.

 Kritibas said: (Oct 29, 2016) W:S = 3:5 after adding water it become 1:1 here there is no change in syrup so multiply 5 * (1:1) = 5/5 so only water is change 2 part now 2/(5 + 5) = 2/10 = 1/5.

 Ujwal said: (Dec 2, 2016) @Murali. Here I want to add something regarding your confusion about the last step. For eg, if we say 2 is what part of 8? Ans is 1/4 and how? ( 2 / 8 = 1/4 ) Similarly 5/8 is what part of 8? Ans is ( (5/8) / 8) i.e (5 / 8) * 1/8 = 1/5.

 Anil said: (Dec 4, 2016) Quantity of syrup is 5. Quantity of water is 3. You have to add and subtract 1 from water quant and syrup quant respectively. Keep that one in numerator and the amount of which has to be reduced (syrup 5) should come in the denominator. 1/5. I have tried with other problems also it worked.

 Jitender said: (Dec 6, 2016) It is simple as Kiran said. Suppose you have total (means 100% solution) is 8 litre. In which you have 5 parts of milk means 60% milk and 3 parts of water means 40% water. Now you have to make mixture 50%-50%. So you have to reduce 10% milk and increase 10% water means if you mix 20% extra water in that then it will reduce quantity of milk 10% and increase water 10% in solution. That's it answer is 20% = 20/100 = 1/5.

 Rushit said: (Jan 5, 2017) Thank you for teaching the new method friends!

 Manisha said: (Jan 6, 2017) Let's consider total mix is100 litre, Water = 3parts = 37.5liter. Syrup = 5parts = 62.5 litre. We have to draw liquid so that syrup remains. 50 litre for that we have to draw out the quantity of mixture which contains 12.5 litres of syrup. Now mixture containing 12.5-litre syrup contain = 12.5 * 8/5 = 20 litre. We have to draw out 20litre mix. i.e 20/100 = 1/5 mix have to replace for getting 1:1 mixture.

 Abhijit said: (Jan 30, 2017) w:s 3:5 Consider in tens 30 : 50 3 : 5 1:1 40:40 To get 40 syrup you need to remove 10. as the ratio is 3:5. So, to remove 10 you need to remove 8x2=16 volume of liquid = 16/80 = 1/5.

 Jas said: (Mar 17, 2017) A 10 litre container holds a mixture of water and sugar, the volume of sugar being 15% of total volume. A few litres of the mixture is released and an equal amount of water is added. Then the same amount of the mixture as before is released and replaced with water for a second time. As a result, the sugar content becomes 10% of total volume. What is the approximate quantity of mixture released each time? please solve this sum? Can anyone solve this?

 Shanmukha said: (Mar 30, 2017) Thanks for your active cooperation. It's very helpful.

 Dileep said: (Apr 12, 2017) Let us consider the mixture to be of 8 litres (3 Litres of water + 5 litres of Syrup). Amount of Water in the 8 litre Mixture : 3/8. Amount of Syrup in the 8 litre Mixture : 5/8. For easy calculation, I am considering the mixture to be of 10 litres. Hence Amount of Water in the 10 litre Mixture : 3/8 * 10 = 3.75. Amount of Syrup in the 10 litre Mixture : 5/8 * 10 = 6.25. We need to replace 1.25 litres of syrup from the mixture and replace with water 50 make it 5 / 5. Hence we need to replace 2 litres of mixture (.625+.375) * 2. 2 Litres out of 10 litres is 20% or 1/5.

 Murali D said: (May 19, 2017) Very good explanation, Thanks @Surendrareddy.

 Shriyash Sharma said: (Jun 24, 2017) Formula. Final volume or the ratio of solute A=initial volume or ratio solution A(1-solute to be replaced/total volume)^n. let A=syrup, B=water. Putting in formula: assuming volume is 1litre. A=5/8, B=3/8. applying formula on solute A because it will be reduced after an operation. so, 4/8=5/8(1-x/1), x=1/5.

 Vikas said: (Jul 14, 2017) How did you get that equation 5x+24=40-5x?

 Iptisam said: (Jul 21, 2017) 1/2(y-x)/y. =1/2(5-3)/5, = 1/2 * 2/5, = 1/5.

 Suraj said: (Sep 8, 2017) Thanks @Surendrareddy.

 Mukku said: (Sep 11, 2017) 3 5 \ / 8 / \ 3 5 ratio 3:5. we need to calculate for water only, 3/5*1/3 = 1/5, 1/3 because one portion of water is 1/3.

 Naveen said: (Oct 29, 2017) 1/2* (bib value-small value) /big value. Here, big value=5. Small value = 3. After putting value in above formula, we get, 1/2* (5-3) /5. 1/2* 2/5. 1/5 = 1:5.

 Kashif Kashi said: (Oct 29, 2017) Correct answer for the question asked "how much of the *mixture* must be drawn off" is 8/5 Or 1.6 (which consists of some part or proportion of water and syrup). > while the c option given is the correct answer of "what is the proportion of syrup in the mixture drawn off"=1/5. > while proportion of water in the mixture drawn off = 0.6/3 OR 1/5 (i am proving these below). Proof: As given in the question that total quantity (qty) of mixture in a vessel is 8 liters <3 parts of water + 5 parts of syrup>. Now, we can find through it total ratio of water and syrup in the mixture by this way; 3/8*100 = 37.5% water. 5/8*100 = 62.5% syrup. Let "x" is the quantity of that mixture drawn off. & "y" is the quantity of water replaced. As quantity of mixture drawn off is equal to quantity of replaced water, therefore; => x = y .........(euq-1). Now, if we subtract proportion of water(3x/8) in the mixture drawn off from total quantity contain in the vessel (3) and then add quantity of water replaced which is "y" then it will be equal to half quantity of resulting mixture means last mixture. " => 3 - 3x/8 + y = 1/2 * 8. => 3 -3x/8 + y = 4. => (-3x+8y)/8 = 4-3. => (8y-3x)/8 = 1. => 8y-3x = 8........ (equ-2). now I will put value of "y" from equ-1 in equ-2 to solve for value of "x". => 8x - 3x = 8. => 5x = 8. => x = 8/5 ( this is showing that total quantity of mixture drawn off in liters is 8/5 OR 1.6 ). Now, I will find out ratio or proportion of water and syrup in the mixture drawn off means in this total quantity=1.6. Proportion of water in the mixture drawn off =3/8 * 1.6 = 0.6 ltrs. Proportion of syrup in the mixture drawn off = 5/8 * 1.6 = 1 ltrs OR (1.6 - 0.6). Total quantity of syrup drawn of is 1 out of 5 which in terms of proportion will be write as 1/5. Quantity of water drawn of is 0.6 out of 3 which in terms of proportion will be = 0.6/3 OR 1/5. Now, total quantity of syrup after drawn off = 5 - 1 = 4 liters (half of total quantity 8 liters). Like wise quantity of water after drawn off and replaced with water = 3 - 0.6 + 1.6 = 4 liters (half of total quantity 8 liters).

 Fazle Rasool said: (Nov 6, 2017) Given : w:s=3:5, After removal of x litter the ratio becomes w:s=1:1, Quantity of water before and after is, 3/8 - 3x/8 +x = 1/2. 5x/8 = 1/8. x = 1/5 this is the answer and it is a simple method.

 Tamilanda said: (Nov 7, 2017) 5 parts be taken as 50%. 3 parts be taken as 30%. Equal parts syrup and water be taken, Then water increased to 20% . Therefore 20 /100 = 1/5.

 Priyanka said: (Nov 19, 2017) Initially W : S=3:5. After adding water W:S=1:1 Since only water is adding Qty of Syrup will change. W:S=3:5. W:S=5:5. Difference in water =2 part. Total =(5+5)=10 part. 2/10=1/5 Ans.

 Vivek said: (Dec 14, 2017) Can we assume xth part of the mixture be removed and replaced by water?

 Ullas said: (Jan 4, 2018) Can anyone do it by allegation method?

 Priyanka said: (Jan 22, 2018) Thanks @Kiran & @Jitender.

 Neel Mitra said: (Feb 3, 2018) Initially, there were 3/8 water, We will remove 3x/18 from water and add x water [x is the qty of the liquid which was removed.] So new water = 3/8 - 3x/8 + x The same way we can say new syrup 5/8 - 5x/8, So the equation will be 3/8 - 3x/8 + x = 5/8 - 5x/8, (3 - 3x + 8x)/8 = (5-5x)/8, 3 + 5x = 5 - 5x, 10x = 2, x = 1/5; so 1/5 is the answer.

 Manoj said: (Feb 21, 2018) water : syrup=3:5 requeired 1:1 3:5::a:b=1;1 3b=1 5a=1 a=1/5.

 Gowthami said: (Mar 9, 2018) @Guru. The explanation is very impressive. Thankyou.

 Manisha Dambe said: (Mar 19, 2018) We know that water is 3 part and syrup is 5 part. So total amount of mixture must be multiple of 8, If we take 40 lit mixture. It must contain 15 lit water and 25 lit syrup. Now we have to make it 1:1. i.e-20 lit water and 20 lit syrup. Now we have to draw 5 lit of syrup from the mix. When we drew out 8 lit of mix then only it contains 5 lit syrup. 8 lit of water added to the mix makes water and syrup 1:1. 8 out of 40 is 1/5.

 Mounika said: (Apr 28, 2018) Can anyone explain, how it is obtained? (3(x-y)/8)+y=5 (x-y)/8.

 Confused Soul said: (May 20, 2018) Answer: 1/5th of the vessel volume. Let's assume the capacity of vessel be (3+5=) 8 litres. Now, the basic principle of all such questions is that when you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself. So, let's suppose we take x litresout of the vessel. This means 5x/8 amount of syrup and 3x/8 amount of water gets removed. which means the remaining mixture has (3-(3x/8)) litres of water & (5-(5x/8)) syrup. Now when we add x litres of water to this mixture, the amount of water and syrup becomes equal. Thus, (x+3-(3x/8)) = (5-(5x/8)) => x=1.6 ltrs. Since we assumed that vessel is 8 ltrs. in volume=> 1.6/8 = 1/5th of the mixture in the vessel needs to be replaced with water. Hope it helps.

 Mahfujul Hoque said: (May 31, 2018) Good explanation, it is very helpful, Thanks @Victor.

 Kavya.Gv said: (Jul 11, 2018) Excellent explanation @Surendrareddy.

 Nandu said: (Jul 15, 2018) Water : 3 Syrup : 5 & mix = half water & half syrup. 3:5. [(Diff between 3 & 5) 1:1 *5, 5:5, 2/10= 1/5. (2= diff between 3 & 5) (10= 5+5). I Hope this is the easy method.

 Revathi said: (Aug 2, 2018) @Surrendar. Nice explanation, thanks.

 Naveen Gaddam said: (Aug 23, 2018) In Mixture: 3 parts = water and 5 parts=Syrup. Given: 5 parts of Syrup(S) ====> 3 parts of Water(W). So, for 5 parts of Syrup --> 3 parts Water. How much for 1 part Syrup --> water=? 1 part syrup= 3/5=0.6 water. We need to remove 1 part water and 0.6 part syrup and replace with water to equal the mixture= 4S+4W. The removal mixture of 1.6 parts which is 20% of 8 parts = 20% = 20/100 = 1/5.

 Flora said: (Aug 23, 2018) 3/8+5/8x=1/2, 5/8x=1/8, x=1/5.

 Kabali Khan said: (Aug 25, 2018) Nice, Thanks @Flora.

 Kabalai Khan said: (Aug 29, 2018) 3:5 is the ratio given take the largest number in it which is 5. as per question half of milk and syrup so, 5:5 in large number. See the difference which is 2 of the taken ratio is 10 so answer is 1/5.

 Himanshu321_Hani said: (Sep 6, 2018) The Formula is /2*[Big value -small value/ Big value].

 Onupom Deb said: (Sep 25, 2018) NOTE: Liquid = Mixed substance (water, syrup). Let the volume of the vessel = x litres. Out of this x liters 3/8 (x) is water & 5/8 (x) is syrup. Let y litres of liquid is taken out. So out of this, y litres 3/8 (y) is water and 5/8 (y) is syrup. The water in the remaining liquid is 3/8 (x-y). The syrup in the remaining liquid is 5/8 (x-y). Now, y litres of water is added to the remaining liquid so that the final liquid contains half water and half syrup. => 3/8 (x-y) +y=5/8 (x-y). =>y=1/5 (x). Or y = 1/5 (x). Answer: The amount of liquid drawn out = The amount of water added = 1/5 of x.

 Umesh said: (Oct 28, 2018) 1/5 of 8 is 1.6 ------->remaining=6.4. We have to remove 1/5 of liquid and add 1/5 of water(1.6 of water). 1/5 of 3=.6 -----> remaining=2.4. 1/5 of 5=1 -----> remaining=4. 6.4 of liquid =2.4 of water + 4 of syrup. Which means add 1.6 of water to make to make composition equal and 1.6 is 1/5 of 8.

 Mohanish said: (Nov 22, 2018) Given : 3 part is water. 5 part is syrup. Therefore the total mixture content becomes 8. We want the half of this complete mixture means half water and half syrup. So if we add 1 in 3 parts we get 4 i.e. 4/8 = 1/2. And if we subtract 1 from 5 again we get 4 i.e 4/8= 1/2. Therefore we get the half-half content of the water and syrup. In percentage, we added 10% and reduced 10% therefore 10% + 10% = 20%. And 20% = 20/100. So, we get 1/5.

 Suresh said: (Dec 8, 2018) It's simple, but we can't understand what's meaning of question so the meaning of the question is how syrup is removed in the mixture. So they said half water +half syrup=8. Then syrup remove is 5-4 =1. Then in ratio 1/5 parts of syrup is removed that's it.

 Karthik said: (Dec 17, 2018) Let take 5 parts of syrup as 50% of the liquid and 3 parts of water as 30% of the liquid. In order to make both the liquids equal, we have to reduce syrup by 10% and raise water by 10%. So, the total quantity of water we have to add or quantity of liquid we have to draw is 20% which is 1/5 of the liquid.

 Vikas said: (Jan 12, 2019) Initially we have 3 :5 ratio of w:s. We are replacing only water so syrup quantity will remain same. we want mixture in half that is mixture ratio of w: s will be 1:1 but we know syrup quantity won't change so multiply mixture ratio in order to get same quantity of syrup as before i.e. 5 so multiply mixture ratio by 5 we get final ratio of water to syrup (w:s)=5:5. So, initially 3:5 finally 5:5 from above we can say that 2 part of water changing and no of a part in the final mixture is 5+5=10 part. So, 2/10 =1/5.

 Aditya Pandita said: (Jan 21, 2019) @All. The reason in the last step 8/5 is multiplied with 1/8 (or you could say 8/5 is divided by 8) is because we have found x in liters and the answer is required in parts. The 8 that we have used to divide in the last step is not the total 8 parts but it is the 8 liters we have assumed in the beginning of the answer.

 Mouli Ejj said: (Apr 27, 2019) Total mixture=3+5=8. Take lcm of 1/3+1/5=8/5. The hole 8/5 dived by 8 -----> 8/5/8. 8/5*1/8 = 1/5.

 Sheela David said: (Jun 14, 2019) Can you explain? How can we say that mixture drawn off would be 3/8y and 5/8x?

 Mansi said: (Jun 21, 2019) Very helpful, thanks for helping @Surendrareddy.

 Tanmay said: (Aug 3, 2019) Can anyone Explain the formula used in these question?

 Mir said: (Aug 30, 2019) When a mixture is drawn, both syrup and water is drawn equally. So, if 1 part from water and 1 part of syrup(total 2 parts) is drawn, the ratio of 3:5 becomes 2:4. When replaced wit 2 parts of water, gives the ratio 4:4 i..e 1:1. Therefore mixture drawn is 2/8 or 1/4.

 Tanzid said: (Nov 23, 2019) 3:5 becomes 4:4, So change in syrup is (5-4) in 5 units so = 1/5.

 Santosh said: (Mar 8, 2020) Assume 30L water. 50L syrup. Remove 20L liquid. Than water will be 20L and syrup is 40L. Add this 20L to water than 40L and 40L. 20/100 = 1/5.

 Andy said: (Apr 3, 2020) The ratio of water/syrup is 3:5. So, 3/8-3x/8+x = 5/8-5x/8 Solving X, we get 1/5.

 Shivangi said: (Apr 26, 2020) Final(syrup)=initial(syrup)*(1-(qt_replaced/total_mix). X is a mixture replaced with water. p is the total quantity of mixture. 4/8=5/8(1-x/p). We need to find x/p which is 1/5 i.e answer.

 Sriman said: (Jun 30, 2020) Can anyone please explain how 8/5X1/8 come? Please explain.

 Tinku said: (Aug 15, 2020) Can anyone tell me, how to find a total mixture here?

 Twinkle said: (Sep 13, 2020) Simply; (3/8) - (3x/8) + x = (4/8); This will give x = 1/5.

 Abinash Swain said: (Sep 24, 2020) 3 : 5 is given. 1:1 we need, 3 : 5 1*5 : 1* 5 Difference 3 to 5 = 2 Total now 5+ 5 Then 2/ 10 ans is 1/5.

 Sravya said: (Sep 30, 2020) To make the given 3:5 equal we can take out 1 from 5 and add to 3(4:4). Since 1 is taken out from syrup so, the answer will be 1/5.

 Tejas said: (Oct 19, 2020) According to me, the solution is; Water : syrup 30. :50 Total =80 then if x ltr mixture we tack out then the remaining ratio will be 1:1 .So Take option 1/4 then try 1/4of 80 =20, or we can say 20/80*100= 25% of every (water and syrup). But here we get vale in fraction, 25%of 30 = 7.5 ., 25%of 50= 12.5, so this value. 30 - 7.5 =. 22.5 50 - 12.5 = 37.5 + 20 = 57.5. This value not in ratio 1:1. So, here ve take vale 1/5 or we can say 20 %of every part. 30*1/5=6 50 * 1/5 = 10. Thus. 50 - 10 = 40. 30 + 10 = 40 this is in Ratio 1:1.

 Vishesh said: (Nov 9, 2020) The ratio of syrup and water is 3:5 after replacing it will half-half(equal) -> 1:1 Because we are adding only water so the ratio of syrup will be same then ratio 1:1 become 5:5 means 2 ratio water is adding, total ratio is 5 + 5=10. So 2/10=1/5

 Devis said: (Jan 10, 2021) Let us say that the quantity in the vessel is 8x units. It has 3x water and 5x syrup. Now, let's say we withdraw 8y units of the mixture are replace them with water. When we take out 8y units of the mixture, we are actually taking out 3y water and 5y syrup. We are adding pure water back into the vessel. New quantity of syrup = 5x - 5y. New quantity of water = 3x - 3y + 8y = 3x + 5y. They are equal to each other. => 5x - 5y = 3x + 5y. => 2x = 10y, => y/x = 2/10 = 1/5, => 8y/8x = 1/5k. So, 1/5th of the mixture should be taken out and replaced with water.

 Gokul Ramakrishnan said: (Apr 23, 2021) Well said, nice answer. Thanks @Kiran.

 Raavan said: (May 10, 2021) Actually here is a simple way of solving. As there are total 8 parts (3 parts water and 5 parts syrup), the question is that how much quantity of water is added to make both water and syrup half each, frankly speaking, there is no need to remove water as it is to be added again so 1 part of syrup is removed and added as water, so 1 part of 5 parts is 1/5. That's simple.

 Radhakrishnan said: (Jun 13, 2021) Hey, their is a simple way. Using the left value rule Left value= intial value * (1- fraction replaced) We need to find fraction replaced, Left v = 1/2. Initial value = 5/8. Therefore; 1/2 = 5/8 * (1-f). 4/5 = 1-f. f = 1/5.

 Saru Priya said: (Jul 12, 2021) @Kiran. Nice explanation.

 Prakash said: (Aug 20, 2021) Well said, Thank you so much @Ameer.