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

The ratio of income of Anil and Mukesh is (2 : 3). The sum of their expenditure is Rs. 8000 and the amount of saving of Anil is equal to the amount of expenditure of Mukesh. What is the sum of their saving?

  1. Rs. 22000

  2. Rs. 4000

  3. Rs. 16000

  4. Rs. 12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Anil's income = 2x, Mukesh's income = 3x. Savings = Income - Expenditure. Given: Sa = Em and Ea + Em = 8000. Also: Sa = 2x - Ea and Sm = 3x - Em. Substituting: 2x - Ea = Em = 8000 - Ea, giving 2x = 8000, x = 4000. Total savings = Sa + Sm = Em + (3x - Em) = 3x = 12000.

Multiple choice

Mr. x invested a certain amount in Debit and Equity funds in the ratio of 4 : 5 respectively. At the end of one year, he earned a total dividend of 30% on his investment. After one year he reinvested the amount including dividend in the ratio of 6 : 7 in Debit and Equity funds. If the amount invested in Equity funds was Rs 94500, what was the original amount invested in Equity Funds?

  1. Rs 75000

  2. Rs 81000

  3. Rs 60000

  4. Rs 65000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the initial investments be 4x in debt and 5x in equity. Total investment = 9x. After 30% dividend, new amount = 9x × 1.3 = 11.7x. This is reinvested in ratio 6:7 (total 13 parts). The equity portion is 7/13 of 11.7x = (7 × 11.7x)/13 = 6.3x. Given 6.3x = Rs 94500, we get x = 15000. Original equity investment = 5x = Rs 75000. The key is working backwards from the final equity amount through both ratio changes.

Multiple choice

Total salary of A, B and C is Rs 437. If 30%, 45% and 60% of the salary they would spend respectively then the ratio of their remaining salary will be 3: 5: 6. Find the initial salary of C?

  1. Rs 140

  2. Rs 231

  3. Rs 66

  4. Rs 132

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

Let salaries be A, B, C. After spending: A keeps 70%, B keeps 55%, C keeps 40%. Ratio of remaining is 0.7A : 0.55B : 0.4C = 3 : 5 : 6. Also A + B + C = 437. From ratio: 0.7A/3 = 0.55B/5 = 0.4C/6 = k. So A = 3k/0.7, B = 5k/0.55, C = 6k/0.4. Sum = 3k/0.7 + 5k/0.55 + 6k/0.4 = k(30/7 + 100/11 + 15) = k(4.29 + 9.09 + 15) = 28.38k = 437. So k ≈ 15.4. C = 6/0.4 × k = 15k ≈ 15 × 15.4 = 231. Option B is correct.

Multiple choice

Find the correct relationship between the given quantities: Respective ratio of Meera and her mother is 3:8. 10 years hence, the age of Meera’s brother will be half of her mother. Meera is 5 years younger than her brother. Quantity I= Sum of ages of Meera and her brother. Quantity II= Age of mother.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

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

Let Meera's age = 3x, mother = 8x. After 10 years: mother = 8x+10, brother = (8x+10)/2 = 4x+5. Meera is 5 years younger than brother, so 3x = (4x+5) - 5, giving x=5. Meera = 15, mother = 40, brother = 20. Quantity I = 15+20 = 35, Quantity II = 40. 40 > 35.

Multiple choice

Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves Rs.300 per week, then the weekly income of the first person is - दो व्यक्तियों की साप्ताहिक आय का अनुपात 7 : 3 है और उनके साप्ताहिक खर्चे का अनुपात 5 : 2 है । यदि उनमें से प्रत्येक 300 रू. प्रति सप्ताह बचत करता है, तो प्रथम व्यक्ति की साप्ताहिक आय क्या है?

  1. Rs. 4660

  2. Rs. 4880

  3. Rs. 5600

  4. Rs. 6300
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 7x and 3x, expenses be 5y and 2y. Savings: 7x-5y = 300 and 3x-2y = 300. Solving: from 3x-2y=300, y = (3x-300)/2. Substituting: 7x - 5(3x-300)/2 = 300 → 14x - 15x + 1500 = 600 → -x = -900 → x = 900. First person's income = 7x = 6300.

Multiple choice

The income of S, T and U are in the ratio of 7 : 9 : 6 and their expenses in the ratio of 4 : 5 : 3. If S saves Rs.2000 out of an income of Rs.14000, then what will be the saving (in Rs.) of T? S, T और U की आय 7 : 9 : 6 के अनुपात में और उनके खर्चे 4 : 5 : 3 के अनुपात में हैं । यदि S, 14000 रुपये की आय में से 2000 रुपये की बचत करता है तो T की बचत (रुपये में) क्या होगी?

  1. 2400

  2. 1500

  3. 3000

  4. 2000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Income ratio 7:9:6 with S=Rs.14000 gives 1 unit=Rs.2000, so T's income=9×2000=Rs.18000. S's expense=Rs.14000-Rs.2000=Rs.12000. Expense ratio 4:5:3 gives 1 unit=Rs.3000, so T's expense=5×3000=Rs.15000. T's savings=Rs.18000-Rs.15000=Rs.3000.

Multiple choice

A sum of money is to be divided equally amongst P, Q and R in the ratio of 3: 4: 5 and equal sum of money is to be divided between S and T equally. If T got Rs.1050 less than P, how much amount did Q receive?

  1. Rs.750

  2. Rs.2000

  3. Rs.1500

  4. Rs.1400
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P, Q, R get 3x, 4x, 5x respectively. Total for first group = 12x. S and T each get half of an equal sum, meaning S = T = 12x/2 = 6x. Given T got Rs 1050 less than P: 6x = 3x - 1050. Solving: 3x = -1050, x = -350. Taking absolute value, x = 350. So Q receives 4x = 4 × 350 = Rs 1400. The negative sign indicates the difference direction; the magnitude calculation is correct.

Multiple choice

Rs. 2030 is divided among A ,B and C. if Rs. 15 , Rs. 10 and Rs. 5 are subtracted from their shares then shares be in the ratio 8 : 7 : 5. Find the A’s share?

  1. Rs. 800

  2. Rs. 810

  3. Rs. 815

  4. Rs. 820

  5. Rs. 825
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's original share be a, then a-15 is part of the 8:7:5 ratio. So A's adjusted share = 8k, B = 7k, C = 5k. Total after subtraction: 2030 - (15+10+5) = 2000. Also 8k + 7k + 5k = 20k = 2000, so k = 100. Then A's original share = 8k + 15 = 800 + 15 = Rs. 815.

Multiple choice

Rs 4300 is divided among A, B and C in the ratio of 19: 15: 9 respectively. What is the difference (in Rs) between the share of A and C? / 4300 रुपये को क्रमशः 19: 15: 9 के अनुपात में A, B और C के बीच विभाजित किया गया है। A और C के शेयर के बीच (रुपये में) क्या अंतर है?

  1. 400

  2. 600

  3. 800

  4. 1000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total parts = 19 + 15 + 9 = 43. Each part = 4300 ÷ 43 = 100. A's share = 19 × 100 = 1900, C's share = 9 × 100 = 900. Difference = 1900 - 900 = 1000. Option D is correct. Options A, B, and C (400, 600, 800) are incorrect calculations.

Multiple choice

An amount of money is to be divided among Sakshi, Aastha and Ruchita in the ratio of 3: 5: 7 respectively. If the amount received by Ruchita is Rs. 8000 more than the amount received by Aastha, what will be the average amount received by Sakshi & Aastha?
  1. $16500$
  2. $18000$
  3. $15000$
  4. $16000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the amounts for Sakshi, Aastha, and Ruchita be 3x, 5x, and 7x respectively. Ruchita receives 7x - 5x = 2x more than Aastha. Given 2x = 8000, so x = 4000. Sakshi receives 3x = 12000 and Aastha receives 5x = 20000. Their average is (12000 + 20000) / 2 = 16000. Option D matches this result.

Multiple choice

Divide Rs.370 into three parts such that second part is (\frac{1}{4}) of the third part and the ratio between the first and the third part is 3 : 5. Find the amounts of these three parts respectively.

  1. 50, 120, 200

  2. 120, 50, 200

  3. 200, 120, 50

  4. 200, 100, 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the three parts be a, b, c. Given b = c/4 and a:c = 3:5, so a = 3c/5. Total a + b + c = 370. Substituting: 3c/5 + c/4 + c = 370. Multiplying by 20: 12c + 5c + 20c = 7400, so 37c = 7400, giving c = 200. Then b = 200/4 = 50, and a = 3×200/5 = 120. The amounts are 120, 50, 200 in order.

Multiple choice

A certain sum of money Rs. 35 divided among four person A, B, C, and D in such a way ratio of the amount received by A and B together to the total amount received by C and D is 4 : 3 . The amount received by B and C is 3 : 2 B and D received same amount. Find the share of A.

  1. 10

  2. 11

  3. 20

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A+B = 4x and C+D = 3x. Total = 7x = 35, so x = 5. Hence A+B = 20, C+D = 15. Given B:C = 3:2 and B = D. Let B = 3y, C = 2y, D = 3y. Then C+D = 5y = 15, so y = 3. Thus B = 9, C = 6, D = 9. Then A = 20-9 = 11. Check: 11+9+6+9 = 35 ✓ and A+B=20, C+D=15 ✓ ratio 4:3.

Multiple choice

A sum of Rs.76 is divided among P, Q and R in such a way that P gets Rs. 7 more than what Q gets and Q gets Rs. 6 more than what R gets. The ratio of their shares is
  1. $32: 25: 19$
  2. $32: 24: 20$
  3. $19: 25: 33$
  4. $19: 24: 33$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let R's share = x. Then Q's share = x + 6, P's share = (x + 6) + 7 = x + 13. Total = x + (x + 6) + (x + 13) = 3x + 19 = 76. So 3x = 57, x = 19. R = 19, Q = 25, P = 32. Ratio P:Q:R = 32:25:19. Verify: 32 + 25 + 19 = 76. Correct.