Quantitative Aptitude

Ratio and Proportion

775 Questions
All Dividing a total in a given ratio 393 Income, expenditure, and equal-savings equations 117 Ratio changes with constant sum/difference 89 Combining ratios 72 Finding a missing term in a proportion 54 Direct, inverse, and power variation 29 Mean proportional 9 Compound, duplicate, and root ratios 8 Componendo and dividendo 2

Ratio and Proportion Questions

Multiple choice

The ratio of the earnings of A and $\mathrm { B }$ is $ 4: 7 .$ If the earnings A increase by 50$\%$ and those of B decrease by 25$\% $, the new ratio of their earnings becomes $ 8: 7 .$ What are A's earnings?
  1. Rs. $21,000$
  2. Rs. $26,000$
  3. $\mathrm { Rs } .28,000$

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let earnings be 4x and 7x. New earnings are 4x * 1.5 = 6x and 7x * 0.75 = 5.25x. The ratio 6x / 5.25x = 6 / 5.25 = 600 / 525 = 8/7. Since the ratio is satisfied for any x, the actual earnings cannot be determined without a specific total or value.

Multiple choice

The ratio of income of two persons is $9:7$ and the ratio of their expenditure is $4:3$. If each of them saves Rs. $200$ per month, find their monthly income.
  1. Rs. $2200$, Rs. $1400$
  2. Rs. $2100$, Rs. $1400$
  3. Rs. $1800$, Rs. $1400$
  4. Rs. $1900$, Rs. $1400$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Income ratio 9:7, Expenditure ratio 4:3. Let incomes be 9x, 7x and expenditures be 4y, 3y. Savings: 9x - 4y = 200 and 7x - 3y = 200. Multiply first by 3 and second by 4: 27x - 12y = 600 and 28x - 12y = 800. Subtracting: x = 200. Incomes are 9(200)=1800 and 7(200)=1400.

Multiple choice

Divide Rs. 4,260 into three parts proportional to $\displaystyle {2\frac{1}{2}\, :\, 1\frac{2}{3}\, :\, 1\frac{3}{4}}$.
  1. Rs. $1,800$ ;  Rs.$1,200$ and Rs.$1,260$
  2. Rs.$1,600$ ; Rs.$1,200$ and Rs.$1,260$
  3. Rs.$1,800$ ; Rs.$1,200$ and Rs.$1,280$
  4. Rs.$1,800$ ; Rs.$1,400$ and Rs.$1,260$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratios are 5/2 : 5/3 : 7/4. Multiply by LCM(2,3,4)=12 to get 30 : 20 : 21. Total parts = 71. 4260 / 71 = 60. Parts are 30*60=1800, 20*60=1200, 21*60=1260.

Multiple choice

Three person's A, B and C whose salaries together are Rs. $14400$ and expenditures are $80\%$, $85\% $ and $75\%$ of their salaries respectively. If their savings are in the ratio $8:9:20$ , then find their respective salaires.
  1. Rs.$ 3000$, Rs. $5000,$ Rs$. 6400$
  2. Rs. $3400$, Rs. $4800$, Rs. $6200$
  3. Rs. $3200$, Rs. $4800,$  Rs. $6400$
  4. Rs. $3000$, Rs. $5200,$  Rs. $6200$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let salaries be S1, S2, S3. Savings are 20% of S1, 15% of S2, 25% of S3. Ratio 0.2S1 : 0.15S2 : 0.25S3 = 8 : 9 : 20. Solving this with S1 + S2 + S3 = 14400 gives S1 = 3200, S2 = 4800, S3 = 6400.

Multiple choice

15 men, 18 women and 12 boys working together earned Rs 2070 If the daily wages of a man, a woman and a boy are in the ratio 4 : 3 : 2 the daily wages ( in Rs) of 1 man, 2 women and 3 boys are

  1. 135

  2. 180

  3. 240

  4. 205
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the wages be 4x, 3x, and 2x. Total earnings = 15(4x) + 18(3x) + 12(2x) = 60x + 54x + 24x = 138x. Given 138x = 2070, so x = 15. The wages for 1 man, 2 women, and 3 boys = 1(4*15) + 2(3*15) + 3(2*15) = 60 + 90 + 90 = 240.

Multiple choice

A man divided two sums of money among 4 sons R, S, T, U the first in the ratio 4 : 3 : 2 : 1 and the second in the ration 5 : 6 : 7 : 8 If the second sum of money is twice the first the first sum which son receives the largest part?

  1. R

  2. S

  3. T

  4. U
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The first sum is divided in ratio 4:3:2:1 (total 10 parts). The second sum is divided in ratio 5:6:7:8 (total 26 parts). Let the first sum be S1 and the second be S2 = 2*S1. R's share is 0.4*S1 + (5/26)*2*S1 = 0.4*S1 + 0.384*S1 = 0.784*S1. Comparing shares, R receives the largest portion.