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 of money has to be divided between two persons P and Q in the ratio 3 : 5 .But it was divided in the ratio of 2 : 3 and thereby Q loses Rs. 10 .What was the amount ?

  1. Rs. 250

  2. Rs.300

  3. Rs. 350

  4. Rs.400
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total amount = x. Q's share in 3:5 ratio = 5x/8, in 2:3 ratio = 3x/5. Loss: 5x/8 - 3x/5 = (25x-24x)/40 = x/40 = 10, so x = 400. Verification: In 3:5, Q gets 250; in 2:3, Q gets 240. Loss = 10.

Multiple choice

P, Q and R's monthly income is in the ratio of 53 : 70 : 57. Q's annual income is Rs. 420000 then what is the sum of annual income of P and R ? P, Q और R की मासिक आय के बीच अनुपात क्रमशः 53 : 70 : 57 है। Q की वार्षिक आय रू. 420000 है, तो P और R की वार्षिक आय का योग क्या है ?

  1. Rs.660000

  2. Rs.600000

  3. Rs.720000

  4. Rs.640000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Q's annual income = Rs. 420000, so monthly income = 420000/12 = Rs. 35000. Monthly ratio P:Q:R = 53:70:57. Q's share (70 parts) = 35000, so 1 part = 500. P's monthly = 53 × 500 = 26500, R's monthly = 57 × 500 = 28500. Annual sum of P and R = (26500 + 28500) × 12 = 55000 × 12 = Rs. 660000.

Multiple choice

Two numbers P and Q are such that the sum of 5% of first number and 4% of second number is two-third of the sum of 6% of first number and 8% of second number. Find the ratio between P and Q. दो संख्याएं P और Q इस प्रकार हैं कि पहली संख्या के 5% और दूसरी संख्या के 4% का योग पहली संख्या के 6% और दूसरी संख्या के 8% के योग का दो तिहाई है। P और Q के बीच अनुपात ज्ञात कीजिये।

  1. 2 : 1

  2. 1 : 2

  3. 1 : 1

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

Given: 0.05P + 0.04Q = (2/3)(0.06P + 0.08Q). Multiply by 300: 15P + 12Q = 12P + 16Q. Simplify: 3P = 4Q, so P/Q = 4/3. The ratio P:Q is 4:3. The claimed answer is correct.

Multiple choice

A sum is divided among P, Q and R such that if their respective shares are increased by Rs. 120, Rs. 150 & Rs. 90 respectively, their shares becomes in the ratio (9 : 8 : 6) & the total amount becomes Rs. 2300. Then initial shares were in the ratio of ?

  1. 6 : 5 : 4

  2. 78 : 65 : 51

  3. 71 : 63 : 57

  4. 7 : 6 : 5

  5. 39 : 32 : 27
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial shares be 9x-120, 8x-150, 6x-90 (to become 9:8:6 after increases). Total: 9x-120+8x-150+6x-90 = 23x-360 = 2300. So 23x = 2660, x ≈ 115.65. Initial shares: 9(115.65)-120 ≈ 920.85, 8(115.65)-150 ≈ 775.2, 6(115.65)-90 ≈ 603.9. Ratio ≈ 920.85:775.2:603.9 ≈ 78:65.6:51.1 ≈ 78:65:51. Option B matches.

Multiple choice

A and B's income are in the ratio 3 : 2 and their expenses are in the ratio 5 : 3. If each of them saves Rs. 2000, then the income of A is : A तथा B की आय 3 : 2 के अनुपात में है और उनके खर्च 5 : 3 के अनुपात में हैं। यदि उनमें प्रत्येक 2000 रू. की बचत कर लेता हो, तो A की आय कितनी है?

  1. Rs. 8000

  2. Rs. 10000

  3. Rs. 12000

  4. Rs. 15000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's income be 3x and B's income be 2x. Let A's expenses be 5y and B's expenses be 3y. Since each saves Rs 2000, we have 3x - 5y = 2000 and 2x - 3y = 2000. Solving these equations gives y = 2000 and x = 4000, so A's income = 3(4000) = Rs 12000.

Multiple choice

The ratio of Ekta’s and Reema’s income last year was 10:3. The ratio of Ekta’s this year income and last year income is 6:5 and the ratio of Reema’s this year income and last year income is 2:3. If the sum of Ekta’s and Reema’s present incomes is Rs. 5,124, what was Reema’s income last year?

  1. Rs. 1464

  2. Rs. 1830

  3. Rs. 1098

  4. Rs. 1654

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

Let last year's income of Ekta = 10x, Reema = 3x. This year: Ekta = 10x × 6/5 = 12x, Reema = 3x × 2/3 = 2x. Total present income = 12x + 2x = 14x = 5124, so x = 366. Reema's income last year = 3x = 3 × 366 = 1098.

Multiple choice

Railway fare of AC , Sleeper and General class between two station is 8 : 6 : 3. The fares of AC and Sleeper are subsequently reduced by 1/6 and 1/12 respectively. If during this year, the ratio between the passenger of AC , Sleeper and General class was 9 : 12 : 26 and total amount collected by the sale of tickets was Rs. 1088 lakh , then find the collection from the passenger of AC?

  1. 320 lakh

  2. 355 lakh

  3. 387 lakh

  4. 410 lakh

  5. 425 lakh
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original ratio 8:6:3. AC reduced by 1/6 becomes 8×5/6=20/3. Sleeper reduced by 1/12 becomes 6×11/12=11/2. New fares 20/3:11/2:3 = 40:33:18. Passenger ratio 9:12:26. Revenue: 9×40 + 12×33 + 26×18 = 360+396+468 = 1224 parts. AC collection = (360/1224)×1088 = 320 lakh.

Multiple choice

Four years ago, the ratio of ages of A and B is 5 : 6 and five years after the ratio will become 6 : 7, then Quantity I: present age of A Quantity II: age of B 4 years ago

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

4 years ago: A=5x, B=6x. Present: A=5x+4, B=6x+4. 5 years after present: (5x+4+5):(6x+4+5) = 6:7 → 5(x+9) = 6(x+9) is impossible. Correct: (5x+9):(6x+9) = 6:7 → 35x+63 = 36x+54 → x=9. A present = 5(9)+4 = 49. B 4 years ago = 6(9) = 54. 54 > 49, so Quantity II > Quantity I.

Multiple choice

According to the will, the wealth of Rs 110400 was to be divided between the son and the daughter in the ratio 2/3 : 5/4. Find the difference of share of son and daughter. वसीयत के मुताबिक 110400 रुपये की संपत्ति बेटे और बेटी के बीच 2/3: 5/4 के अनुपात में विभाजित की जानी थी। बेटे और बेटी के हिस्से का अंतर ज्ञात कीजिये।

  1. 32800 Rs./रुपये

  2. 40200 Rs./रुपये

  3. 33600 Rs./रुपये

  4. 31400 Rs./रुपये
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The correct answer is C. First, simplify the ratio 2/3 : 5/4 to get whole numbers. Multiplying both fractions by 12 (LCM of 3 and 4): (2/3) × 12 : (5/4) × 12 = 8 : 15. This means the wealth is divided in the ratio 8:15 between son and daughter. Total parts = 8 + 15 = 23. Total wealth = Rs 110,400. Value of one part = 110400 ÷ 23 = Rs 4,800. Son's share = 8 × 4800 = Rs 38,400. Daughter's share = 15 × 4800 = Rs 72,000. Difference = 72000 - 38400 = Rs 33,600. Option A (32800), B (40200), and D (31400) are incorrect.

Multiple choice

A sum of Rs.9260 is divided among 8 men, 9 women and 12 boys. If share of each man, each woman and one boy are in the ratio 6 : 4 : 3, find the share of each boy. 9260 रु, की एक धनराशि को 8 आदमी, 9 महिलाओं और 12 बच्चों में बांटी जानी है | यदि एक आदमी का हिस्सा, एक महिला के हिस्से और एक एक बच्चे के हिस्से में अनुपात 6 : 4 : 3 है, प्रत्येक बच्चे का हिस्सा ज्ञात कीजिये |

  1. Rs.213.5

  2. Rs.231.5

  3. Rs.230.5

  4. Rs.215.3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total share units = 8×6 + 9×4 + 12×3 = 48 + 36 + 36 = 120. Value of 1 unit = 9260/120 = Rs. 77.17. Each boy's share = 3 units = 3×77.17 = Rs. 231.5. Option B is correct.

Multiple choice

Rs.30525 was to be divided among A, B and C in the ratio 1 4 : 1 5 : 1 6 . But by mistake it was divided in the ratio of 4: 5: 6. The amount in excess received by C was 30525 रु. को A, B और C में 1 4 : 1 5 : 1 6 के अनुपात में बांटा गया लेकिन गलती से इसको 4: 5: 6 के अनुपात में बाँट दिया गया तो C द्वारा कितनी राशि अधिक प्राप्त की गयी ।

  1. Rs.3960

  2. Rs.4125

  3. Rs.1210

  4. Rs.2860
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Intended ratio: 1/4 : 1/5 : 1/6 = 15:12:10 (LCM method). Actual ratio: 4:5:6. Total = 30525. Intended for C: 10/37 × 30525 = 8250. Actual for C: 6/15 × 30525 = 12210. Excess = 12210 - 8250 = 3960.

Multiple choice

The ratio of monthly income of A and B is 76 : 71. If income of A is increased by Rs. 500 and income of B is increased by Rs 625, then ratio becomes 20 : 19. What is the A's monthly income before increment?

  1. Rs. 7550

  2. Rs. 8200

  3. Rs. 8875

  4. Rs. 9500

  5. Rs. 9950
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A's income be 76x and B's income be 71x. After increases: (76x + 500)/(71x + 625) = 20/19. Cross-multiply: 19(76x + 500) = 20(71x + 625). Solve: 1444x + 9500 = 1420x + 12500. 24x = 3000, so x = 125. A's income = 76 × 125 = Rs. 9500.

Multiple choice

If Rs. 8400 is divided among A, B and C in the ratio 1 5 : 1 6 : 1 10 , what is the share of A? यदि 8400 रू. को A, B और C में 1 5 : 1 6 : 1 10 के अनुपात में बाँटना हो, तो A का हिस्सा क्या है?

  1. Rs.1800

  2. Rs.3000

  3. Rs.3600

  4. Rs.4000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio 1 5 : 1 6 : 1 10 is written ambiguously. As printed, it reads 15:16:110 with sum 141 parts. A's share = (15/141) × 8400 = Rs. 893.61... which is not an option. If interpreted as fractions 1/5:1/6:1/10, the LCD ratio is 6:5:3 with sum 14 parts. A's share = (6/14) × 8400 = Rs. 3600, matching option C. The spacing suggests fractions.

Multiple choice

A sum of Rs.10600 is divided among P, Q, R in such a way that P gets Rs.1400 more than what Q gets and Q gets Rs.1600 more than what R gets. The ratio of their shares is रु.10600 की राशि P, Q, R के मध्य इस तरह से विभाजित की जाती है कि P को Q से 1400 रुपये अधिक मिलते हैं और Q को R से 1600 रुपये अधिक मिलते हैं | उनके भागों का अनुपात है

  1. 16 : 9 : 18

  2. 27 : 18 : 10

  3. 25 : 18 : 10

  4. 16 : 25 : 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R's share be x. Then Q gets x + 1600 and P gets x + 1600 + 1400 = x + 3000. Their total is x + (x + 1600) + (x + 3000) = 3x + 4600 = 10600. Solving gives x = 2000, so R = 2000, Q = 3600, P = 5000. The ratio P:Q:R simplifies from 5000:3600:2000 to 25:18:10. Option A (16:9:18) and D (16:25:10) don't match this pattern.