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

In a class the ratio of the number of boys to that of the girls is $7: 3$. Each boy is given only a $50$ paise coin and each girl is given a $75$ paise coin (assuming $75$ paise coins are available) The difference in the amount present with the boys and the girls is Rs. $3.75$. How many coins should the boys and girls exchange so that the amount with the boys becomes twice the amount with the girls?
  1. $8$
  2. $6$
  3. $4$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boys be 7x and girls be 3x. Boys have 350x paise, girls have 225x paise. Difference 125x = 375, so x = 3. Boys have 21, girls 9. Total amounts are 1050 and 675. After exchanging coins, the ratio must be 2:1. Solving for the number of coins leads to 4.

Multiple choice

There is $34000$ rupees in a beg in the denomination of $Rs 50,Rs 100,Rs 500$ and $Rs 1000$ currencynotes. If the ratio of the number of these notes is $2:3:4:1$ then find the number of notes of $500$ denomination.
  1. $20$
  2. $40$
  3. $30$
  4. $50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of notes be 2x, 3x, 4x, and 1x. Value = 50(2x) + 100(3x) + 500(4x) + 1000(x) = 100x + 300x + 2000x + 1000x = 3400x. Given 3400x = 34000, x = 10. Number of 500 notes is 4x = 40.

Multiple choice

Two numbers are in the ratio $17:45$. One third of the smaller is less than $\displaystyle \frac{1}{5}$ of the bigger by 15. The smaller no is
  1. $\displaystyle 25\frac{12}{2}$
  2. $\displaystyle 67\frac{12}{2}$
  3. $\displaystyle 76\frac{1}{2}$
  4. $\displaystyle 86\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the numbers be 17k and 45k. The condition gives 45k/5 - 17k/3 = 15, so k = 4.5. The smaller number is therefore 17 × 4.5 = 76.5, or 76 1/2.

Multiple choice

The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70%, 60% and 50% respectively from their salaries. If the balance with them are into Ratio 1:2:3, what is the salary of each?

  1. A Rs. 300; B Rs. 500; C- Rs. 700

  2. A Rs. 200; B Rs. 300; C- Rs. 650

  3. A Rs. 100; B Rs. 300; C- Rs. 600

  4. A Rs. 400; B Rs. 600; C- Rs. 720
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let salaries be S_A, S_B, S_C. Savings are 0.3S_A, 0.4S_B, 0.5S_C. Ratio 0.3S_A : 0.4S_B : 0.5S_C = 1:2:3. 0.3S_A = k, 0.4S_B = 2k, 0.5S_C = 3k. S_A = 10k/3, S_B = 5k, S_C = 6k. Sum = (10/3 + 5 + 6)k = 1720. (43/3)k = 1720. k = 120. S_A = 400, S_B = 600, S_C = 720.

Multiple choice

A man who makes a profit of $25\ p.c.$ by selling tea at $Rs. 4.25$ a kg lowers his ratio so as to gain only $17\ P$ per kg. In what ratio must his sales increase so that the profit may be the same as before?
  1. $4$ times
  2. $5$ times
  3. $7$ times
  4. $85$ times
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At Rs. 4.25 per kg and 25% profit, the cost price is Rs. 3.40, so the profit is Rs. 0.85 per kg. A profit of 17 paise per kg requires five times as many kilograms to earn the same total profit.

Multiple choice

The total of the daily wages of Ram, Shyam and Mohan is $Rs. 450$. If they, respectively spend $25\%, 20\%$ and $50\%$ of their incomes then the ratio of their savings becomes $9 : 8 : 4$. What is the income of Ram?
  1. $180$
  2. $190$
  3. $200$
  4. $175$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let incomes be R, S, M. R+S+M = 450. Savings: R(1-0.25)=0.75R, S(1-0.20)=0.8S, M(1-0.5)=0.5M. Ratio 0.75R : 0.8S : 0.5M = 9:8:4. 0.75R/9 = 0.8S/8 = 0.5M/4 = k. R=12k, S=10k, M=8k. 12k+10k+8k=450 -> 30k=450 -> k=15. R = 12*15 = 180.

Multiple choice

In a family the ratio of expenses to the savings is $5 :3$. But his expenses is increased by $60\%$ and income is increased by only $25\%$ thus there is decrease of $Rs. 3500$ in the saving. Find the increased income of the family.
  1. $Rs. 35000$
  2. $Rs. 28000$
  3. $Rs. 25000$
  4. $Rs. 18,500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let expenses be 5x and savings be 3x, so income is 8x. New expenses = 5x * 1.6 = 8x. New income = 8x * 1.25 = 10x. New savings = 10x - 8x = 2x. The decrease in savings is 3x - 2x = x = 3500. The new income is 10x = 10 * 3500 = 35000.

Multiple choice

The cost of manufacturing of an article consists of material, labor and overheads cost which are in the ratio $4 : 3 : 2$. If the cost of labor is Rs.$ 45$, find the total cost the article. Also, find the profit percent, if the article is sold for Rs. $180$.
  1. $191;\, \displaystyle 12\frac{1}{5}$%
  2. $191;\, \displaystyle 19\frac{1}{5}$%
  3. $135;\, \displaystyle 33\frac{1}{3}$%
  4. $135;\, \displaystyle 43\frac{1}{3}$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio 4:3:2. Labor cost (3 parts) = 45, so 1 part = 15. Total cost = (4+3+2) * 15 = 135. Profit = 180 - 135 = 45. Profit percent = (45/135) * 100 = 100/3 = 33 1/3%.

Multiple choice

I derive an annual income of Rs 688.25 from Rs 10000 invested partly at 8% p.a, and partly at 5% p.a. simple interest. What is the ratio of my money invested at 5% to the investment at 8%.
  1. $114 : 165$
  2. $51 : 58$
  3. $97 : 113$
  4. $149 : 251$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount at 8% and y be the amount at 5%. We have x + y = 10000 and 0.08x + 0.05y = 688.25. Solving this system gives 0.03x = 688.25 - 500 = 188.25, so x = 6275 and y = 3725. The ratio of 5% investment to 8% investment is 3725 : 6275, which simplifies to 149 : 251.