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

Rs 8000 is distributed among A, B and C such that they receive notes of Rs 500, Rs 200 and Rs 100 respectively. The amounts received by them are in the ratio 15: 2: 3. What was the ratio of the number of notes of Rs 500, Rs 200 and Rs 100?
  1. $3: 1: 3$
  2. $3: 3: 1$
  3. $4: 1: 2$
  4. $3: 2: 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratio of amounts is 15:2:3. Let amounts be 15x, 2x, 3x (total = 20x = 8000, so x = 400). A gets 6000 in Rs 500 notes = 6000/500 = 12 notes. B gets 800 in Rs 200 notes = 800/200 = 4 notes. C gets 1200 in Rs 100 notes = 1200/100 = 12 notes. Ratio of notes = 12:4:12 = 3:1:3.

Multiple choice

The amount of Rs 22750 is divided between P, Q, R, S in such a way that the ratio of parts of P and Q, Q and R, and R and S is equal to 2: 3. Profit of R is: 22750 रूपए की राशि P, Q, R, S के बीच में इस प्रकार विभाजित किया जाता है कि P और Q, Q और R तथा R और S के हिस्सों का अनुपात 2: 3 के बराबर है| R का हिस्सा है:

  1. 2800

  2. 4200

  3. 5400

  4. 6300

  5. None of these इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P, Q, R, S be the amounts. P/Q = 2/3, Q/R = 2/3, R/S = 2/3. So P = 2x, Q = 3x, R = 4.5x, S = 6.75x (each is 1.5 times the previous). Total: 16.25x = 22750. x = 1400. R = 4.5 × 1400 = 6300.

Multiple choice

The income of Neel and Kamal of last year in the ratio of 4:3 respectively. The ratios of their individual incomes of the last year and the present year are 3:4 and 5:6 respectively. If their total income of the present year is Rs 34840. Then find last year income of Kamal?

  1. 11700

  2. 12700

  3. 13700

  4. 14700
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Neel's and Kamal's last year incomes be 4x and 3x respectively. Their present year incomes are in ratio 3:4 and 5:6 respectively, so Neel's present income = 4x·(4/3) = 16x/3, and Kamal's present income = 3x·(6/5) = 18x/5. Total present income = 16x/3 + 18x/5 = (80x + 54x)/15 = 134x/15 = 34840, so x = (34840·15)/134 = 3900. Kamal's last year income = 3x = 3 × 3900 = 11700.

Multiple choice

A ,B and C spends 4/5, 17/20 and 3/4 of their incomes respectively. If the ratio between their savings is 8 : 9 : 20 and income of C is Rs. 18,000 more than income of A, then find the income of B?

  1. Rs 36,000

  2. Rs 30,000

  3. Rs 27,000

  4. Rs 24,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's income be x. A saves 1/5 of income (spends 4/5), B saves 3/20 of income (spends 17/20), and C saves 1/4 of income (spends 3/4). Given savings ratio 8:9:20, we have A's savings = k/5, B's savings = 3k/20, C's savings = k/4. The ratio (k/5):(3k/20):(k/4) = 4:3:5, but given ratio is 8:9:20. Scaling: 8/4 = 2, 9/3 = 3, 20/5 = 4. So incomes are 2x:3x:4x. Since C earns Rs. 18,000 more than A: 4x - 2x = 18000, x = 9000. B's income = 3x = Rs. 27,000.

Multiple choice

A sum of money is divided between A, B, C and D such a way that the ratio of A and B is 2:3, B:C is 1:2 and C:D is 3:4. If share of D is Rs 648 more than the share of A, then find the total money?

  1. Rs 2,484

  2. Rs 1,944

  3. Rs 2160

  4. Rs 2052
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A:B = 2:3, B:C = 1:2 = 3:6, C:D = 3:4 = 6:8. Combined ratio A:B:C:D = 2:3:6:8. Let shares be 2k, 3k, 6k, 8k. Given D - A = 8k - 2k = 6k = Rs. 648, so k = 108. Total = 2k + 3k + 6k + 8k = 19k = 19 × 108 = Rs. 2,052. This matches option D.

Multiple choice

The monthly incomes of two persons are in the ratio 2 : 3 and their monthly expenses are in the ratio 5 : 9. If each of them saves Rs 600 per month then the total of their monthly incomes are - दो व्यक्तियों की मासिक आय का अनुपात 2 : 3 है और उनके मासिक व्यय का अनुपात 5 : 9 है। यदि उनमें से प्रत्येक 600 रू. प्रति माह की बचत करता है तो उनकी मासिक आय का योग क्या है?

  1. Rs. 4800 4800 रू

  2. Rs. 4000 4000 रू

  3. Rs. 4500 4500 रू

  4. Rs. 4200 4200 रू

  5. Rs. 5000 5000 रू
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Incomes = 2x, 3x. Expenses = 5y, 9y. Savings: 2x - 5y = 600 and 3x - 9y = 600. From first: 2x = 600 + 5y → x = 300 + 2.5y. Substitute: 3(300 + 2.5y) - 9y = 600 → 900 + 7.5y - 9y = 600 → 900 - 1.5y = 600 → 1.5y = 300 → y = 200. Then x = 300 + 500 = 800. Incomes: 1600, 2400. Total = 4000. Option B is correct.

Multiple choice

The income of A and B are in the ratio of 4:7. A and B saves Rs. 4000 and 5000 respectively. If the expenditure of A is equal to 60% of the expenditure of B. Then, find the difference between their incomes.

  1. 10,000

  2. 12,000

  3. 15,000

  4. 20,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 4x and 7x for A and B respectively. Expenditure = Income - Savings. A's expenditure = 4x - 4000. B's expenditure = 7x - 5000. Given: A's expenditure = 0.6 × B's expenditure, so 4x - 4000 = 0.6(7x - 5000). Solving: 4x - 4000 = 4.2x - 3000, giving -1000 = 0.2x, so x = 5000. A's income = 20000, B's income = 35000. Difference = 35000 - 20000 = 15000.

Multiple choice

The income of Suresh and Rakesh are in the ratio 5 : 4 and their expenditure are in the ratio 3 : 2. If each saves Rs. 6000, then Suresh’s income can be: सुरेश और राकेश की आय 5: 4 के अनुपात में है और उनका खर्च 3: 2 के अनुपात में है। यदि प्रत्येक 6000 बचाता है , फिर सुरेश की आय हो सकती है:

  1. 12000

  2. 15000

  3. 16000

  4. 10000

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

Let Suresh's income = 5x and Rakesh's income = 4x. Let their expenditures be 3y and 2y respectively. Savings = Income - Expenditure. For Suresh: 5x - 3y = 6000. For Rakesh: 4x - 2y = 6000. Solve the system: From the second equation, 2y = 4x - 6000, so y = 2x - 3000. Substitute in first: 5x - 3(2x - 3000) = 6000, giving 5x - 6x + 9000 = 6000, so x = 3000. Suresh's income = 5x = 5 × 3000 = Rs. 15000.

Multiple choice

The ratio of income of Praveen to Qureshi is 5:7. If Qureshi's income is increased by 35%, his total income becomes Rs. 52,920. Then find the income of Praveen? प्रवीण से कुरैशी की आय का अनुपात 5: 7 है। अगर कुरैशी की आय 35% बढ़ जाती है, तो उसकी कुल आय रु 52,920 हो जाती है । तो प्रवीण की आय ज्ञात कीजिये?

  1. Rs. 27350

  2. Rs. 28000

  3. Rs. 23000

  4. Rs. 17260

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

Qureshi's final income = 52920 (after 35% increase). So Qureshi's original income = 52920 ÷ 1.35 = 39200. Praveen:Qureshi = 5:7, so Praveen's income = (5/7) × 39200 = 28000. The ratio applies to original incomes, not the increased amount.

Multiple choice

The incomes of A, B and C are in the ratio 3 : 7 : 4 and their expenses in the ratio 4 : 3 : 5. If A saves Rs. 300 out of an income of Rs. 2,400, the savings of B and C are A, B और C की आय 3: 7: 4 के अनुपात में है और उनका खर्च 4: 3: 5 के अनुपात में है। यदि A एक 2400 रु. की आय में से 300 रु. की बचत करता है, B और C की बचत है

  1. Rs. 4025 and/और Rs. 575

  2. Rs. 1575 and/और Rs 2.625

  3. Rs. 2750 and/और Rs. 1.525

  4. Rs. 3725 and/और Rs. 1.525
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A saves Rs. 300 from income Rs. 2400, so A's expense = 2400 - 300 = 2100. Income ratio is 3:7:4, expenses ratio is 4:3:5. If A's income (3 parts) = 2400, then 1 part = 800. B's income (7 parts) = 7×800 = 5600. B's expense (3 parts) = (3/4)×2100 = 1575. So B saves 5600 - 1575 = Rs. 4025. C's income (4 parts) = 4×800 = 3200. C's expense (5 parts) = (5/4)×2100 = 2625. So C saves 3200 - 2625 = Rs. 575. Option A matches these values.

Multiple choice

Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question? What is Ashok's monthly salary? (I) Ashok's monthly salary is Rs 2400 more than the Varun's monthly salary. (II) The ratio between the monthly salary of Varun and Pratap is 4 : 7. (III) Pratap's annual salary is Rs 168000.

  1. Only II

  2. Only I

  3. Either II or III

  4. All I, II and III
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From Statement III: Pratap's annual salary = Rs 168000, so monthly salary = 168000/12 = Rs 14000. From Statement II: Varun's salary : Pratap's salary = 4 : 7, so Varun's salary = (4/7) × 14000 = Rs 8000. From Statement I: Ashok's salary = Varun's salary + Rs 2400 = 8000 + 2400 = Rs 9200. All three statements are required.

Multiple choice

Daniel had 10 paise, 25 paise and 50 paise coins in the ratio of 5 : 4: 9 respectively. After giving Rs. 30 to his mother he has Rs. 30. How many 50 paise coins did he have?

  1. 50

  2. 90

  3. 70

  4. 80

  5. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let coins be 5x, 4x, 9x for 10p, 25p, 50p. Total value = 5x × 0.10 + 4x × 0.25 + 9x × 0.50 = 0.5x + x + 4.5x = 6x rupees. After giving Rs. 30, remaining = Rs. 30, so original total = Rs. 60. Then 6x = 60, x = 10. Number of 50p coins = 9x = 90.