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

A certain amount was to be distributed among X, Y and Z in the ratio 7 : 3 : 5, but was erroneously distributed in the ratio 4 : 7 : 6. As a result of this, A got Rs. 59 less. What was the amount?

  1. Rs. 210

  2. Rs. 255

  3. Rs. 315

  4. Rs. 520

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

The intended share for X is 7/15 of the total, while the erroneous share is 4/17. Their difference is 59/255 of the total, which equals 59 rupees, so the total amount is 255 rupees.

Multiple choice

Divide Rs. 156 in the ratio 1 : 2 : 4 : 5.

  1. Rs. 13, Rs. 26, Rs. 53 & Rs. 64

  2. Rs. 13, Rs. 26, Rs. 51 & Rs. 66

  3. Rs. 13, Rs. 26, Rs. 52 & Rs. 65

  4. Rs. 13, Rs. 25, Rs. 53 & Rs. 65

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

Total parts = 1 + 2 + 4 + 5 = 12. Value per part = 156 / 12 = 13. The amounts are 1*13, 2*13, 4*13, 5*13, which are 13, 26, 52, 65.

Multiple choice

Divide 672 in the ratio 5 : 3.

  1. 420, 252

  2. 419, 253

  3. 418, 254

  4. 417, 255
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total parts = 5 + 3 = 8. Each part = 672 / 8 = 84. First part = 5 * 84 = 420. Second part = 3 * 84 = 252.

Multiple choice

A sum of money was to be divided among Karan, Ashish and Shallu such that if each of them received Rs. 57 less, then the ratio of their shares became 2 : 5 : 9. If the initial amount to be divided was Rs. 475, then find the share of Shallu.

  1. Rs. 450

  2. Rs. 228

  3. Rs. 426

  4. Rs. 332

  5. Rs. 780
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If each received 57 less, total reduction is 3 * 57 = 171. New sum = 475 - 171 = 304. Ratio 2:5:9 means 16 parts. 1 part = 304 / 16 = 19. Shallu's new share = 9 * 19 = 171. Original share = 171 + 57 = 228.

Multiple choice

Three friends Rajesh, Jatin and Himanshu started their jobs in the year 2011. They got their wages in the ratio 3 : 7 : 4. After a month, they decided to find out how much money they were spending. Their expenditures were in the ratio 4 : 3 : 5. Rajesh saved Rs. 300. His wage was Rs. 2400. How much money might the other two friends have saved?

  1. Rs. 4025 and Rs. 575

  2. Rs. 3025 and Rs. 675

  3. Rs. 2025 and Rs. 757

  4. Rs. 1575 and Rs. 805

  5. Rs. 1125 and Rs. 905
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rajesh's wage is 2400 and his expenditure is 4 units. Since 4 units = 2400, 1 unit = 600. His expenditure is 4 * 600 = 2400, but he saved 300, implying his wage was 2700 (contradicting the 2400 given). Assuming the ratio 3:7:4 applies to wages, if Rajesh (3 parts) earns 2400, 1 part = 800. Jatin earns 5600 and Himanshu earns 3200. Using the expenditure ratio 4:3:5, if Rajesh's expenditure is 2400 - 300 = 2100, 1 unit = 525. Jatin's expenditure is 3 * 525 = 1575, saving 5600 - 1575 = 4025. Himanshu's expenditure is 5 * 525 = 2625, saving 3200 - 2625 = 575.

Multiple choice

P, Q and R completed a piece of work and earned Rs. 2100 in total. P worked for 6 days, Q worked for 4 days and R worked for 9 days. If their daily wages were in the ratio 5 : 6 : 4, then how much money was received by P?

  1. Rs. 700

  2. Rs. 560

  3. Rs. 840

  4. Rs. 1000

  5. Rs. 900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total earnings are proportional to (days * wage_rate). P: 6*5=30, Q: 4*6=24, R: 9*4=36. Total units = 30+24+36 = 90. P's share = (30/90) * 2100 = 700.

Multiple choice

Sam has Rs. 1000 in his pocket in the denominations of Rs. 50 and Rs. 100 only. The ratio of the number of Rs. 50 notes to that of Rs. 100 notes is 25 : 50. How many Rs. 50 notes are there in his pocket?

  1. 10

  2. 20

  3. 4

  4. 8

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

Let the number of Rs. 50 notes be 25k and Rs. 100 notes be 50k. The total value is 50(25k) + 100(50k) = 1250k + 5000k = 6250k. Setting 6250k = 1000 gives k = 1000/6250 = 0.16. The number of Rs. 50 notes is 25 * 0.16 = 4.

Multiple choice

A bag contains coins amounting to Rs. 870 in the denominations of 1-rupee, 50-paisa and 25-paisa in the ratio 3 : 5 : 7. Find the respective number of coins in each denomination.

  1. 240, 720, 800

  2. 360, 540, 800

  3. 360, 600, 840

  4. 360, 600, 800

  5. 450, 750, 1050
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given: A bag containing coins of 1-rupee, 50-paisa and 25-paisa. Coins are in the ratio of 3 : 5 : 7. Let the number of coins of 1-rupee, 50-paisa and 25-paisa be 3x, 5x and 7x, respectively. Value of 1-rupee coins = Rs. (3x × 1) = Rs. 3x Value of 50-paisa or -rupee coins = Rs. = Rs. x Value of 25-paisa or -rupee coins = Rs. = Rs. The bag contains Rs. 870. According to the question, 3x + x + = 870 = 870 = 870 x = 120 1-rupee coins = 3 120 360 50-paisa coins = 5 120 600 25-paisa coins = 7 120 840

Multiple choice

The ratio of the bank balances of three brothers A, B and C is 10 : 12 : 5, respectively. B transfers Rs. 60,000 from his account to C's. The new ratio of the bank balances becomes 10 : 9 : 8. What is the bank balance of A (in Rs.)?

  1. 1,00,000

  2. 2,00,000

  3. 3,00,000

  4. 4,00,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial balances: A=10k, B=12k, C=5k. After B transfers 60k to C, new balances are A=10k, B=12k-60k, C=5k+60k. The new ratio 10:9:8 implies (12k-60k)/(5k+60k) = 9/8. Solving for k: 8(12k-60k) = 9(5k+60k) => 96k - 480k = 45k + 540k. This leads to k = 20,000. A's balance = 10 * 20,000 = 200,000.

Multiple choice

Two brothers A and B had some savings in the ratio of 4 : 5. They decided to buy a gift for their sister, sharing the cost in the ratio of 3 : 4. After they bought the gift, A spent two-third of his amount while B was left with Rs. 26. Then, the price of the gift was

  1. Rs. 140

  2. Rs. 116

  3. Rs. 112

  4. Rs. 105
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial savings be 4x and 5x. Gift cost is 3y and 4y. A spent 2/3 of his money, so 2/3 * 4x = 3y, 8x = 9y, x = 9y/8. B is left with 5x - 4y = 26. Substituting x: 5(9y/8) - 4y = 26. 45y/8 - 32y/8 = 26. 13y/8 = 26, y = 16. Gift cost = 3y + 4y = 7y = 7 * 16 = 112.