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 cricket match there are three types of tickets A, B and C each costing Rs. 1000, Rs. 500 and Rs. 200 respectively. The ratio of ticket sold of category A, B and C is 3 : 2 : 5. If the total collection from selling the tickets is Rs. 2.5 crore. Find the total number of tickets sold?

  1. 5000

  2. 4800

  3. 50000

  4. 52000

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number of tickets be 3x, 2x, 5x. Revenue = 1000(3x) + 500(2x) + 200(5x) = 3000x + 1000x + 1000x = 5000x. Total revenue = 2.5 crore = 25,000,000. 5000x = 25,000,000, so x = 5000. Total tickets = 3x + 2x + 5x = 10x = 50,000.

Multiple choice

A total of \$1,105 is given to three brothers Harry, Caden and Oliver by their uncle Mr. Henry. They divide this sum in such a way that if Harry, Caden and Oliver respectively spend \$10, $20 and $15 from the money they receive, then the ratio of the sums that they have after spending will be 11 : 18 : 24. What is the share that Oliver gets?
  1. $325
  2. $495
  3. $500
  4. $521
  5. $575
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total after spending = 1105 - (10+20+15) = 1060. The ratio 11:18:24 sums to 53 parts. 1060 / 53 = 20. Oliver's share after spending = 24 * 20 = 480. Original share = 480 + 15 = 495.

Multiple choice

A lady has a total of Rs. 75 in her purse. The total amount she has is in denominations of 10 paisa, 25 paisa and 50 paisa coins. The ratio of 10 paisa and 25 paisa coins is 5 : 3 and that of 25 paisa and 50 paisa coins is 6 : 5. What is the number of 10 paisa coins?

  1. 90

  2. 120

  3. 150

  4. 210

  5. 300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the ratios 10p:25p = 5:3 and 25p:50p = 6:5, we normalize the ratios to 10p:25p:50p = 10:6:5. Let the number of coins be 10k, 6k, and 5k; the total value is 0.1(10k) + 0.25(6k) + 0.5(5k) = 75, which simplifies to 1k + 1.5k + 2.5k = 75, so 5k = 75 and k = 15. The number of 10 paisa coins is 10 * 15 = 150.

Multiple choice

The amounts of pocket money of Rohan and Sumit are in ratio 4 : 7. They spend the money in the ratio 3 : 5, respectively. Rohan saves Rs. 500 from his pocket money and Sumit saves Rs. 1,000. Find the pocket money of Rohan and Sumit.

  1. Rohan = Rs. 1,800, Sumit = Rs. 3,150

  2. Rohan = Rs. 2,000, Sumit = Rs. 3,500

  3. Rohan = Rs. 2,400, Sumit = Rs. 4,200

  4. Rohan = Rs. 2,800, Sumit = Rs. 4,900

  5. Rohan = Rs. 1,600, Sumit = Rs. 2,800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let pocket money be 4x and 7x. Spending is 3y and 5y. 4x - 3y = 500 and 7x - 5y = 1000. Multiply first by 5 and second by 3: 20x - 15y = 2500 and 21x - 15y = 3000. Subtracting gives x = 500. Rohan = 4*500 = 2000, Sumit = 7*500 = 3500.

Multiple choice

The incomes of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's savings are one-fourth of his income, then the ratio of savings of A, B and C is

  1. 56 : 99 : 69

  2. 99 : 56 : 69

  3. 69 : 56 : 99

  4. 99 : 69 : 56
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Income ratio 7x:9x:12x. A's savings = 1/4 * 7x = 1.75x. A's expenditure = 7x - 1.75x = 5.25x. Ratio of expenditures is 8:9:15. If 8k = 5.25x, then k = 5.25x/8. B's exp = 9k = 5.90625x. C's exp = 15k = 9.84375x. Savings: A=1.75x, B=9x-5.90625x=3.09375x, C=12x-9.84375x=2.15625x. Ratio 1.75 : 3.09375 : 2.15625 simplifies to 56:99:69.

Multiple choice

The incomes of two persons are in the ratio of 9 : 7 and their expenditures are in the ratio of 4 : 3. If each of them manages to save Rs. 3,000 per month, find the difference in their income.

  1. 10,000

  2. 5,000

  3. 6,000

  4. 3,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Income ratio 9x:7x, Expenditure ratio 4y:3y. Savings: 9x - 4y = 3000, 7x - 3y = 3000. Multiply first by 3 and second by 4: 27x - 12y = 9000, 28x - 12y = 12000. Subtract: x = 3000. Difference in income = 9x - 7x = 2x = 6000.

Multiple choice

Refer to the data table below and answer the following question: Year Ratio Import/Export 2011 0.8 2012 0.8 2013 1.2 2014 1.2 2015 1.5 If the import in 2012 was Rs. 1,200 crore and the total export in the years 2012 and 2013 together was Rs. 3,200 crore, then the import in 2013 was

  1. 1,700 crore

  2. 1,500 crore

  3. 1,417 crore

  4. 2,040 crore
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the 2012 ratio of import to export (0.8) and the 2012 import of Rs. 1,200 crore, we find the 2012 export is 1,200 / 0.8 = Rs. 1,500 crore. Subtracting this from the combined 2012 and 2013 export of Rs. 3,200 crore gives the 2013 export as Rs. 1,700 crore. Finally, using the 2013 ratio of 1.2, the 2013 import is 1.2 * 1,700 = Rs. 2,040 crore.

Multiple choice

The ratio of monthly incomes of Pawan and Sunil is 4 : 3 and the ratio of their monthly expenditures is 3 : 2. If Pawan and Sunil save Rs. 4000 and Rs. 6000 respectively per month, then what is the sum of their monthly incomes?

  1. Rs. 60,000

  2. Rs. 70,000

  3. Rs. 50,000

  4. Rs. 36,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Incomes 4x, 3x. Expenses 3y, 2y. 4x - 3y = 4000; 3x - 2y = 6000. Multiply first by 2, second by 3: 8x - 6y = 8000; 9x - 6y = 18000. Subtract: x = 10000. Total income = 7x = 70000.