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

Out of three numbers, the ratio of the first and the second numbers is 3 : 4 and the ratio of the second and the third numbers is 5 : 6. If the difference between the first and the third numbers is 1125, find the average of the second and third numbers.

  1. 2750

  2. 2507

  3. 2075

  4. 2570
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the three numbers be a, b, c in the ratios 3:4 and 5:6. To combine: a:b = 15:20 and b:c = 20:24, giving a:b:c = 15:20:24. Let k be the common multiplier. Then a=15k, b=20k, c=24k. Difference c-a = 9k = 1125, so k = 125. Average of b and c = (20k+24k)/2 = 22k = 22×125 = 2750. Option A is correct.

Multiple choice

In a wallet, there are notes of the denominations Rs. 10 and Rs. 50 . The total number of notes is 12 . The number of Rs. 10 and Rs. 50 notes are in the ratio of 1:2. Total money in the wallet is:

  1. Rs. 280

  2. Rs. 360

  3. Rs. 440

  4. Rs. 110
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let notes of Rs. 10 be 3x and Rs. 50 be 6x (ratio 1:2). Total notes: 3x + 6x = 12, so 9x = 12, giving x = 4/3. Number of Rs. 10 notes = 3 × 4/3 = 4. Number of Rs. 50 notes = 6 × 4/3 = 8. Total amount = 4 × 10 + 8 × 50 = 40 + 400 = Rs. 440.

Multiple choice

A sum of money is distributed among A, B, C and D in the ratio 5:7:11:15, respectively. If C gets Rs 2,480 more than B, then the difference between the shares of B and D is:

  1. Rs 4690

  2. Rs 6490

  3. Rs 4960

  4. Rs 4950
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let shares be 5k, 7k, 11k, 15k. C gets 11k, B gets 7k. Difference: 11k - 7k = 4k = 2480, so k = 620. B's share = 7 × 620 = 4340, D's share = 15 × 620 = 9300. Difference = 9300 - 4340 = 4960. Options A (4690), B (6490), and D (4950) are calculation errors.

Multiple choice

The ratio between the divisor and remainder is 3 : 2 and the ratio between the divisor and the quotient in 7 : 12. If remainder is 14, then find the remainder when the dividend is divided by 9.

  1. 7

  2. 2

  3. 5

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

Divisor:Remainder = 3:2, Remainder = 14, so Divisor = 21. Divisor:Quotient = 7:12, so Quotient = 36. Dividend = Divisor × Quotient + Remainder = 21 × 36 + 14 = 756 + 14 = 770. When 770 is divided by 9: 770 = 9 × 85 + 5, so remainder is 5.

Multiple choice

By mistake, instead of dividing ₹702 among Ram, Ramesh, and Naresh in the ratio 1/3:1/4:1/6, it was divided in the ratio of 3:4:6. Who gained the most and by how much?

  1. Ram ₹158

  2. Naresh ₹158

  3. Naresh ₹ 168

  4. Ram ₹ 168
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The intended ratio 1/3:1/4:1/6 simplifies to 4:3:2 (total 9 parts). The actual ratio 3:4:6 gives 13 parts. Intended shares: Ram ₹312, Ramesh ₹234, Naresh ₹156. Actual shares: Ram ₹162, Ramesh ₹216, Naresh ₹324. Naresh gained ₹168 (₹324 - ₹156), which is the maximum gain.

Multiple choice

The cost of a piece of diamond varies with the square of its weight. A diamond of Rs.6,084 value is cut into 3 pieces whose weights are in the ratio (3:2:1). Find the loss involved in the cutting.

  1. Rs. 3,768

  2. Rs. 3,718

  3. Rs. 3,168

  4. Rs. 3,518
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the total weight be 6x (ratio 3:2:1). The weights are 3x, 2x, x. Original value varies with square of weight, so value = k × (6x)² = 36kx² = ₹6,084. After cutting, total value = k(9x² + 4x² + x²) = 14kx² = (14/36) × 6084 = ₹2,366. Loss = 6084 - 2366 = ₹3,718.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the monthly income of Rakesh? (I) The total monthly income of Rakesh and Deepti is Rs. 27000 which is 150% of their total monthly expenditure. (II) The ratio of their monthly expenditure is 5:4.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: R + D = 27000 and this is 150% of their expenditure, so (R + D)'s expenditure = 27000/1.5 = 18000. This gives combined expenditure but not individual incomes. Statement II: Expenditure ratio is 5:4, but no absolute values. Combining: If expenditure ratio is 5:4, individual expenditures are 10000 and 8000. But we don't know the income split - only total income is 27000. Without knowing how income relates to expenditure individually, we cannot determine Rakesh's income alone.

Multiple choice

The ratio of earning of A, B, C is 5 : 8 : 13. If the earning of A is increase by 20%, earning of B also increased by some percent and earning of C is decreased by 40% then sum of earning of A, B, C remains same as before. If the difference of initial earning and increased earning of B is Rs. 3360. What was the sum of earning of A, B, C together? A,B, C की आय का अनुपात 5: 8: 13 है। यदि A की आय 20% बढ़ जाती है, B की आय में भी कुछ प्रतिशत की वृद्धि हुई है और C की आय 40% कम हो जाती है तो A,B, C की आय का योग पहले की तरह ही रहता है। यदि B की प्रारंभिक आय और बढ़ी हुई आय अंतर 3360 रूपये है, तो प्रारंभ में A,B, C की आय का योग क्या था ।

  1. Rs. 3360

  2. Rs. 22800

  3. Rs. 20020

  4. Rs. 20800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial earnings be 5x, 8x, 13x (sum = 26x). After changes: A = 6x (+20%), C = 7.8x (-40%). For total to remain 26x, B must earn 12.2x. Difference: 12.2x - 8x = 4.2x = Rs. 3360, so x = 800. Initial sum = 26x = 26 × 800 = Rs. 20800. Options A, B, and C are incorrect.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Naveen and Rajiv are saving money in proportion 4:3 respectively. What is Naveen's saving? I. Rajiv savings is 75% that of Navin's saving. II. Rajiv saving is Rs. 4500.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II gives Rajiv's saving as Rs 4500. Given the ratio 4:3 (Naveen:Rajiv), Naveen's saving = (4/3) × 4500 = Rs 6000. This is sufficient. Statement I only states that Rajiv's saving is 75% of Naveen's, which is the same as the 3:4 ratio - it gives no absolute value.