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
Answer: Option E
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
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:
(Thu, Sep 9, 2010 10:46:24 AM)
I did not get last Step. Could you please explain how it was?
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.
Madhu said:
(Sat, Sep 25, 2010 10:32:11 PM)
Excellent Kiran! Your answer is very nice.
Vigneshwaran K said:
(Wed, Sep 29, 2010 05:29:51 AM)
Hai I can't understand the steps can you please give me the understandable steps.
Thank you.
Nitesh said:
(Thu, Oct 7, 2010 06:45:31 AM)
@ Surendrareddy.
You are rocking. This is the right way.
Uma said:
(Fri, Oct 15, 2010 02:45:39 AM)
I am agree with Siri. Your way of explanation is also excellent. Thanks.
Amuthan said:
(Sat, Oct 16, 2010 08:18:13 AM)
Great work Surendara Reddy.
Bindhureddy said:
(Thu, Oct 28, 2010 04:38:25 AM)
@surendrareddy. Your way of explanation is good. Moreover it is easy to do.
Krishan said:
(Thu, Dec 9, 2010 06:02:46 AM)
@Surender reddy. its nice approach to solve it thanks..
Krishjlk@Gmail.Com said:
(Wed, Dec 15, 2010 11:02:45 PM)
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:
(Wed, Dec 22, 2010 12:02:06 AM)
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:
(Sun, Dec 26, 2010 12:41:54 AM)
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:
(Wed, Feb 2, 2011 10:46:40 PM)
@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:
(Sat, Feb 5, 2011 05:40:06 AM)
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:
(Fri, Feb 11, 2011 12:35:08 AM)
Thanks it is really a good way to solve it.
Ravi said:
(Tue, Mar 1, 2011 09:24:15 AM)
Uttam and surender. Your answer is perfect. Kiran is wrong.
Ameer said:
(Fri, May 6, 2011 11:08:16 AM)
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:
(Sun, May 15, 2011 01:57:47 AM)
Thanks ameer for your detailed explanation...
Manasa said:
(Fri, Jun 10, 2011 07:37:08 AM)
Uttam, surender and ameer has cleared out my confusion regarding this problem. Thanks a lot.
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:
(Sat, Jun 25, 2011 08:36:15 AM)
Here is simple approach
3/5-1/2=1:1
Surya said:
(Fri, Jul 1, 2011 06:39:07 AM)
Can you solve this problem with allegation formula ?
Supreeth said:
(Wed, Aug 31, 2011 06:12:01 PM)
Victor your way of doing this problem is less time consumable. Thank you.
Hari said:
(Wed, Sep 7, 2011 03:18:05 PM)
As kiran said about getting the percentage. How its possible, can you explain it clealy of getting 60%, 40 %.
Preethi said:
(Wed, Sep 14, 2011 07:41:20 PM)
Excellant victor.
Divya said:
(Tue, Sep 20, 2011 10:17:30 PM)
Thanks victor. Your way of explanation is short and simple.
Sunny said:
(Thu, Sep 22, 2011 01:05:18 PM)
Good victor.
Satyam said:
(Wed, Oct 5, 2011 05:51:07 PM)
Thank you kiran.
Vipin Kumar said:
(Thu, Nov 3, 2011 06:21:35 PM)
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:
(Thu, Dec 1, 2011 09:39:18 AM)
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:
(Tue, Jan 3, 2012 12:14:39 AM)
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:
(Sat, Jan 7, 2012 12:46:10 AM)
I think amir done good solution.
Varsha said:
(Wed, Jan 18, 2012 05:29:40 PM)
Thanks ameer.
Vaishali said:
(Sun, Jan 22, 2012 11:58:18 AM)
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:
(Fri, Feb 3, 2012 07:28:42 PM)
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
5x + 24 = 40 - 5x