# Aptitude - Ratio and Proportion - Discussion

### Discussion :: Ratio and Proportion - General Questions (Q.No.6)

6.

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

 [A]. 8 : 9 [B]. 17 : 18 [C]. 21 : 22 [D]. Cannot be determined

Explanation:

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).  120 x 7x and 110 x 8x 100 100 42x and 44x 5 5 The required ratio = 42x : 44x = 21 : 22. 5 5

 K.Kiran Kumar said: (Aug 4, 2010) I can not get that how 120% of 7x and 110% of 8x. Please someone explain it.

 Ramesh said: (Dec 9, 2010) 7:8 can also be written as 70:80 120/100*70 = 84 110/100*80 = 88 so,new ratio= 84 : 88 or 42 : 44 or 21 : 22

 Abhinesh said: (Jan 12, 2011) (7x+0.2*7x)/(8x+0.1*8x)=21:22

 Sripal S said: (Mar 6, 2011) @Kiran Kumar note that something we included to get 20% For example the ratio of the ratio of to boys ages was 5:2 we can write it as 5x : 2x we get exact ratio we will not consider it alone For that way 7x 8x will appear then to covert 20% into no. it will be 20/100 note that the unknown was x then 20/100x*x so we take common one x(20/100+1) so x(20/100+100) x(120/100) that was we get 120/100 forget x because that x which is in 7x both are same so we get 120/100*7x

 Sasha said: (May 6, 2011) I like ramesh's methods ! thanks a lot :).

 Poonma said: (Jun 14, 2011) Ramesh your to good.

 Khushboo said: (Jul 19, 2011) Why do we multiply 120% by 7x and 100% by 8x Why not we simply multiply 20% by 7x and 10% by 8x ? Please someone explain me.

 Raj said: (Aug 9, 2011) RAMESH very well said. ! keep posting your SHORTCUT method. Its very useful for us. !i search at every discussion. Because of you. !

 Priyabrata said: (Sep 26, 2011) 20% of 7=14/10,total increase 7+14/10=84/10 10% of 8=8/10,total increase 8+8/10=88/10 now compare ratio of Boys and Girls 84/10:88/10 or 84:88 or 42:44 or 21:22

 Kavya said: (Sep 29, 2011) I am getting 7:4 by whichever method I do. I am not satisfied with any explanations given. Help me.

 Rajeev said: (Nov 8, 2011) @ ramesh Can you tell you multiply 70 & 80 instead of 7 & 8, as we get same answer in both the cases?

 Prasanna said: (Jan 9, 2012) @rajeev. Yes you get the same answers.

 Sunali said: (Feb 22, 2012) Thanks priyabhrt.

 Pankaj said: (Jul 31, 2012) There is some problem to understand the problem ie question is asked 20% and 10% but here get 120% and 110% why ?

 Zahir said: (Oct 8, 2012) 20%of7 = 7/5 that means boys total = 7+7/5. =42/5. 10%of8 = 4/5 that means girls total = 8+4/5 = 44/5. Boys : Girls = 42/5:44/5. =42:44. =21:22.

 Nive said: (Aug 9, 2013) Simply find 20% of 7 and 10% of 8. It will be 1.4 and 0.8 respectively. So the ratio is 8.4:8.8. Then convert the fraction into whole numbers. If I multiply by 10 I will get 84:88 now we can easily simplify it. So we get 21:22.

 Gowtham said: (Dec 11, 2013) Simply find 20% of 7 and 10% of 8. It will be 1.4 and 0.8 respectively. Till this ok then,how 8.4:8.8. And how to convert it into fraction. So the ratio is 8.4:8.8. Then convert the fraction into whole numbers. If I multiply by 10 I will get 84:88 now we can easily simplify it. So we get 21:22.

 Stark Vin said: (Apr 15, 2014) Hi all, One minor doubt, why we are using for every question for ratio, what x mean? is a assumed value or what ? for this question if we didn't use x also we are getting the answer, but in other cases, we need to use X, please suggest me a good method. Thanks.

 Atul1487 said: (Apr 26, 2014) Boys: Girls. 7:8. 20% increase in boys no. so, 7*20% = 1.4 so total boys = 7+1.4 = 8.4. 10% increase in girls. 8*10% = 0.8 So total Girls = 8+0.8 = 8.8. So Ratio of Boys & Girls. 8.4 : 8.8. 21:22 Answer.

 Md Shahrukh said: (May 24, 2014) Let the no of boys 7 and girls 8. 7x120/100: 8x110/100. 840:880. So answer is 21:22.

 Narayana Rao Gartam said: (Aug 18, 2014) 20% of 70 is 14 (20/100*70) So, Total increase is 84. 10% of 80 is 8 So, total increase is 88. Ratio of 84/88 = 21/22, i.e 21:22.

 Prakash Yadav said: (Aug 30, 2014) 20%of 7 = 1.4 : 10%of 8 = 0.8 . 7+1.4 : 8+0.8; 8.4 : 8.8; 84/10 : 88/10; 42/5 : 44/5; 21 : 22.

 Simran said: (Nov 25, 2014) Can someone give short method?

 Mateen said: (Feb 1, 2015) How 120 and 110 come into the picture? Please explain sir.

 Arvind_Ap said: (Mar 29, 2015) G, B. 7:8 = 70, 80. 20% 10% = 120, 110. G = 70*120 = 840. B = 80*110 = 880. = 84/88 = 21/22. Answer = 21:22.

 Ankita said: (Apr 6, 2015) Why we use decimal values instead of fraction value? 20% of 7 = 7/5. 10% of 8 = 4/5. 7/5:4/5 = 7:4. So answer should be 7+7:4+8 = 14:12.

 Aditya said: (Apr 25, 2015) We also 7:8 is 70:80. So 20% and 10% =120 and 110. Then 70*120 = 840, 110*8 = 880. Simply divide them, 840/880 = 21/22 (Answer).

 Hackersk said: (Jul 22, 2015) How you took ratio 21:22 from 42/5:44/5? How 5 is eliminated please explain?

 Prakash said: (Aug 12, 2015) Please tell me easy steps or tricks to find ratios in complex cases without working a lot of steps! I m waiting! for your reply.

 Swastik said: (May 1, 2016) Thanks @Priyabrata. Your method is easy to solve the problem.

 Moorthi said: (Aug 17, 2016) How you took ratio 21:22 from 42/5 : 44/5? How 5 is eliminated? Please explain.

 Rosy said: (Sep 11, 2016) 42/5 and 44/5 how is it 21 : 22? Please explain in detail.

 Riya said: (Sep 19, 2016) The ratio of the cost price and selling price is 4:5 what is the profit percentage? Does anyone know how to solve this?

 Ajay said: (Oct 11, 2016) 7 * 20/100 = 7/5, 7/5 + 7 = 42/5, 8 * 10/100 = 4/5, 4/5 + 8 = 44/5, 42/5 : 44/5 = 21 : 22.

 Mohanraj said: (Oct 12, 2016) The first ratio is 7 increase proposal is 120 (100% + 20%). The second ratio is 8 increase proposal is 110 (100 + 10%). The ratio is 7 * 120 = 840 : 8 * 110 = 880. The answer of the new ratio is 21 : 22.

 Chaitra said: (Dec 4, 2016) Ramesh sir, how you get 42:44?

 Muhammad Naeem said: (Dec 17, 2016) @Chaitra. 6 * 7 = 42 and 11 * 4 = 44.

 Yamini Saraswathi said: (Feb 8, 2018) Actually, I am getting answer as a (120/100)*7=8.4 so approximately = 8. (110/100)*8=8.8 so approximately = 9. The answer is 8:9.

 Abhishek Bansal said: (Feb 11, 2018) Given : B : G = 7:8. This can be written as 7x : 8x ( X being the common multiplier). Let x = 10 (For simple Calculation) So Boys = 70 & Girls = 80. Increased Of Boys by 20% = 70*20/100 = 14. So After Increase boys would be = 70 + 14 = 84. Similarly Girls = 80*10/100 = 8 & Girls After Increase would be = 80 + 8 = 88. New Boys : New Girls = 84:88. Simply 21:22.

 Pawan said: (Mar 8, 2018) 7+8=15. %= 15+100=150, 7:8 increase by 20% & 10%, 70= 20%=14, 80=10%=8, Therefore, 70+14=84, 80+8=88, 84:88, Divide by 4, Hence new ratio is; 21:22.

 Charan said: (Mar 23, 2018) The total percent of 7x is 100% and they increase 20% so we take it as 120*7x in the same way 110*8x is taken.

 Naresh said: (May 28, 2018) 7*120/100 = 84/10, 8*110/100 = 88/10, 84/10:88/10 = 84:88. 21:22.

 Karthik Pangala said: (Jul 28, 2018) @Stark Vin. We are taking X because ratio means dividing the total quantity into some parts and the number of parts we divide them into is represented in the form of the ratio. For example, if I have 30 chocolates and if I want to divide them in the ratio 1:2 then first I will see into how many equal parts I need to divide the chocolates into that is 3 in this case why? Because ratio is 1:2 that is to parts I want is 3. That means I need to divide 30 into 3 equal parts and then take 1 part on one side and other part on the other side. This simply means if I divide 30 by 3 I get 10. This means I divided 30 into 3 equal parts where each part contains 10 chocolates. Now I need to divide them in the ratio 1:2 so I take 10 chocolate on one side which is one part of 30 in this example and remaining 2 parts which add up to 20 in other parts. Now 10 by 20 equals 1 by 2 or 1:2 that is what we call as ratio. That is ratio is the representation of total quantity in its simplest form. We could have written it as 10:20 by we need to simplify as much as possible so we take it as 1:2. Now coming to this question we have the boys to girls ratio as 7:8 that simply means the total strength was divide into 7+8 parts but since we do not know what is the total strength we take it as some variable say t now, t by 15 we assume as x. This means now I have divided total strength into 15 equal parts were each part contains x. In that 7x we take as number of boys and 8x as number of girls.

 Ruchith Praharsha said: (Sep 12, 2018) Let the no of boys be 7x and no of girls be 8x. If it is increased by 20 and 10 per cent lets take x as 10 they will 70 and 80 and the increase will be 84 and 88 the ratio is 84 :88 that is 21:22.

 Aman said: (Jan 10, 2019) 7 : 8 = 70 : 80. 70 * 120/100 = 84, 80 * 110/100 = 88, So, 84:88 = 21:22.

 Siva said: (Feb 8, 2019) Can you say, how 42/5 : 44/5 = 21:22? Please explain clearly.

 Abhishek Chaturvedi said: (Sep 10, 2019) Let the boys be 7x and girls be 8x. Boys 20 percent = 7x * 20/100 = 7X/5. Girls 10 percent = 8x * 10/100 = 4x/5. Total boys = 7X + 7x/5 = 42x/5. Total girls = 8x+ 4x/5 = 44x/5. So, ratio; Total boys : total girls = 42x/5 /44x/5 = 22/22 = 21:22.

 Ganesh Dey said: (Sep 19, 2019) Please tell me, why denominator 5 is removed?

 Ravi said: (Sep 30, 2019) For boys :- 7+20/100. that is 36/5. And for girls:- 8+10/100.that is 81/10. Then ATQ. 36/5*10/81. And answer will become 8:9.

 Yudhisthira Sarapuria said: (Oct 27, 2019) 20% increase mean 120/100 = 6/5.

 Raghual R said: (Dec 27, 2019) We can write 7:8 as 7x and 8x . If x = 1000. Then 7000 : 8000. 20% of 7000 = 1400 then total boys = 7000+1400 = 8400; 10% of 8000 = 800 then total girls = 8800. So the new ratio is 8400:8800 which is 21:22.

 Sam said: (May 30, 2020) Given 7:8. They said there is 20% and 10% increase in this ratio Which means with this 7 , there is 20% increase of 7 .similarly for 8 That is; 7 + 7 * 20/100 : 8+8*10/100. 7+ 7/5 : 8+4/5, 21:22.

 Waquar said: (Aug 11, 2020) Thanks @Priyabrata.