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 man bought total 68 chocolates of 3 different varieties in the ratio 5:10:2.If per chocolate price of these varieties is in the ratio 2:3:5 and he paid a total amount of Rs 400,then find the money spend on these varieties separately?

  1. 40,120,30

  2. 20,80,40

  3. 80,240,80

  4. 80, 220,50

  5. 80, 120,50
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let chocolates be 5x, 10x, 2x = 68 total. So 17x = 68, x = 4. Chocolates: 20, 40, 8. Price ratios 2:3:5. Let prices be 2y, 3y, 5y per chocolate. Total cost: 20×2y + 40×3y + 8×5y = 40y + 120y + 40y = 200y = Rs 400. So y = 2. Individual costs: Variety 1: 40y = 40×2 = Rs 80. Variety 2: 120y = 120×2 = Rs 240. Variety 3: 40y = 40×2 = Rs 80. Option C (80, 240, 80) matches.

Multiple choice

The ratio between the two numbers is 3: 4. The sum of the one - fourth of square of smaller number and half of the square of larger number is 1476. Find the value of the cube root of the product of the numbers. दो संख्याओं में अनुपात 3 : 4 है | छोटी संख्या के वर्ग के एक चौथाई और बड़ी संख्या के वर्ग के आधा का योग 1476 है | संख्याओं के गुणनफल का घनमूल ज्ञात कीजिये |

  1. 12

  2. 13

  3. 14

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let numbers be 3x and 4x. Then (1/4)(3x)² + (1/2)(4x)² = 1476. This gives (9/4)x² + 8x² = 1476, so (41/4)x² = 1476. Thus x² = 144 and x = 12. The numbers are 36 and 48, their product = 1728, and cube root of 1728 = 12.

Multiple choice

The ratio between income of P and Q is 15:17 .when P gives rs 2000 to Q then ratio becomes 7 : 9 .find the total income of P and Q.

  1. 32000

  2. 64000

  3. 48000

  4. 46000

  5. 120000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P's income = 15x and Q's income = 17x. When P gives Rs 2000 to Q, P's income becomes 15x - 2000 and Q's becomes 17x + 2000. The new ratio is 7:9, so (15x - 2000)/(17x + 2000) = 7/9. Cross-multiplying: 9(15x - 2000) = 7(17x + 2000), which gives 135x - 18000 = 119x + 14000. Solving: 16x = 32000, so x = 2000. Total income = 15x + 17x = 32x = 32 × 2000 = 64000.

Multiple choice

In Mr. Pandey's family the ratio of expense to savings is 5 : 3. But his expense increases by 80% and income increases by 25%. Thus there is a deficit of Rs.4236 in his savings. The increased income of Mr. Pandey's family is?

  1. 23460 Rs

  2. 32540 Rs

  3. 21180 Rs

  4. 25480 Rs

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

Let expense = 5x and savings = 3x, so income = 8x. After 80% increase, new expense = 5x × 1.8 = 9x. After 25% increase, new income = 8x × 1.25 = 10x. New savings = 10x - 9x = x. Deficit = old savings - new savings = 3x - x = 2x = 4236, so x = 2118. Increased income = 10x = 10 × 2118 = Rs. 21180.

Multiple choice

A certain amount of Rs 8000 was lent out at 8% per annum and the rest amount is lent out at 18% per annum. After 5 years the total interest (simple intersest) received from the both amounts is Rs4800. What is the ratio of the amount lent out at 8% to the total amount?

  1. 3 : 5

  2. 2 : 5

  3. 3 : 2

  4. 5 : 3

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

Let amount at 8% be x. Amount at 18% is (8000-x). Simple interest after 5 years: SI at 8% = x × 8% × 5 = 0.4x. SI at 18% = (8000-x) × 18% × 5 = 0.9(8000-x) = 7200 - 0.9x. Total SI = 0.4x + 7200 - 0.9x = 7200 - 0.5x = 4800. Solving: 0.5x = 2400, x = 4800. Ratio of amount at 8% to total = 4800:8000 = 3:5. Answer A is correct.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? How much did Shyam earn? (I) Ram, Shyam and Sandeep together earned Rs. 79200. (II) The ratio of earning Ram and Shyam is 2:1. (III) The ratio of Shyam and Sandeep is 3:2.

  1. Only I and II

  2. Only I and III

  3. All I, II and III

  4. Only II and III

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

All three statements are needed. Let Shyam's earning be the common link. From (II), if Ram:Shyam = 2:1, and from (III) Shyam:Sandeep = 3:2, we can set Shyam = 6x. Then Ram = 12x and Sandeep = 4x. From (I), 12x + 6x + 4x = 79200, so 22x = 79200, giving x = 3600. Shyam earns 6x = Rs. 21600.

Multiple choice

The question given below contain three 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 salary of Pravin? I. Pravin earns Rs. 1200 more than Amal. II. The ratio between Amal and Vimal’s monthly salary is 5 : 3. III. Vimal earns Rs. 1000 less than Amal.

  1. Any two

  2. Only I and II

  3. Only II and III

  4. All I, II and III

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

From statements II and III: Amal : Vimal = 5 : 3 and Vimal = Amal - 1000. Solving gives Amal = Rs. 2500 and Vimal = Rs. 1500. Using statement I: Pravin = Amal + 1200 = Rs. 3700. All three statements are needed - II and III give Amal's salary, then I gives Pravin's salary relative to Amal. Only I or only II is insufficient, and II+III alone give Amal but not Pravin.

Multiple choice

Cost of two watches were in a ratio of 16 : 23. The cost of first watch increases by 10% and that of second by Rs. 477.Now the cost of two watches are in a ratio of 11 : 20. The price of the second watch (in Rs.) in the beginning was-

  1. 932

  2. 1696

  3. 848

  4. 1219
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original costs be 16x and 23x. After changes: 17.6x/(23x+477) = 11/20. Solving gives x = 53.09, so second watch initially = 23×53.09 ≈ 1219. The ratio equations and percentage increase lead to option D.

Multiple choice

The ratio of earning of Aaditya and Bhuwan is 5:6. If the earnings of Aaditya decreases by 25% and the earnings of Bhuwan increases by 20% the new ratio becomes 6:11. What is Bhuwan earnings per month?

  1. Rs. 20660

  2. Rs. 23440

  3. Rs. 25500

  4. Rs. 27650

  5. Can’t be determine
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Initial ratio 5:6 means Aaditya = 5k, Bhuwan = 6k. After changes: Aaditya = 5k × 0.75 = 3.75k, Bhuwan = 6k × 1.2 = 7.2k. New ratio = 3.75k : 7.2k = 3.75 : 7.2 = 375 : 720 = 25 : 48. But the problem says new ratio is 6:11. 25/48 ≠ 6/11 (since 25×11=275, 48×6=288). The data is inconsistent, so Bhuwan's earnings cannot be uniquely determined.

Multiple choice

The sum of the income of A, B, C is Rs.72000, if they expense 80% , 85% and 75% and the ratio of their savings is 8 : 9 : 20. Then find the salary of A.

  1. Rs. 20000

  2. Rs. 16000

  3. Rs. 22000

  4. Rs. 18000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be A, B, C. Savings = (1 - expense%) x income. So A_savings = 0.2A, B_savings = 0.15B, C_savings = 0.25C. Given 0.2A : 0.15B : 0.25C = 8 : 9 : 20. Solving: 0.2A = 8k, so A = 40k. 0.15B = 9k, B = 60k. 0.25C = 20k, C = 80k. Total A+B+C = 180k = 72000, so k = 400. Thus A = 40 x 400 = 16000.

Multiple choice

Bhanu borrowed a sum of money from Siddhu at the rate of 9% for 2 years. Later he borrowed an additional sum of money at the rate of 10% for another three more years. If the ratio of the principal amount borrowed is 2 : 6 and the total interest received by Siddhu is Rs. 8100 then what was the total amount paid by Bhanu to Siddhu?

  1. 27000 Rs.

  2. 30000 Rs.

  3. 45000 Rs.

  4. 32100 Rs.

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

Let the amounts borrowed be 2x and 6x. First loan: 2x at 9% for 2 years = 2x × 0.09 × 2 = 0.36x. Second loan: 6x at 10% for 3 years = 6x × 0.10 × 3 = 1.8x. Total interest = 0.36x + 1.8x = 2.16x = Rs 8100, so x = 8100/2.16 = 3750. Total principal = 2x + 6x = 8x = 8 × 3750 = Rs 30000. Total amount = Principal + Interest = Rs 30000 + Rs 8100 = Rs 32100.

Multiple choice

The ratio of income of A to B is 6: 7. A and B, combining their savings, decided to go to a restaurant, and divided the expenditure in the ratio of 4: 3, respectively. If B has spent 140 rupees, which is 20% of its income, then what is the income of A?

  1. Rs 540

  2. Rs 600

  3. Rs 480

  4. Rs 420

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

B's expenditure is 140 rupees, which is 20% of B's income. So B's income = 140/0.20 = 700 rupees. The ratio of A's income to B's income is 6:7. If A's income = 6x and B's income = 7x, then 7x = 700, giving x = 100. Therefore A's income = 6 × 100 = 600 rupees. The information about expenditure division ratio (4:3) is irrelevant to finding A's income.

Multiple choice

In 2007 the ratio of prices of mustard oil and Refined oil were in the ratio of 6:5. In 2008 the price of mustard oil is four times of itself and the price of Refined oil is increased by Rs. 100, then the new ratio of prices of the same oil becomes 4:5. What was the original price of the Refined oil in 2007?

  1. Rs.40

  2. Rs.20

  3. Rs.50

  4. Rs.30

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

Let 2007 prices be 6x (mustard) and 5x (refined). In 2008: mustard = 4(6x) = 24x, refined = 5x + 100. New ratio 24x:(5x + 100) = 4:5. Cross-multiplying: 120x = 20x + 400, so 100x = 400, giving x = 4. Original refined price = 5(4) = Rs. 20.

Multiple choice

The value of a diamond is Rs 40000, which is the directly proportional to the square of its weight. For some reason the diamond fall and is broken into two parts in the ratio of 1: 3. Find out the loss percentage on diamond.

  1. 0%

  2. 32%

  3. 35%

  4. 37.5%

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

When value is proportional to the square of weight, breaking causes significant value loss. Let original weight be 4x (parts x and 3x). Original value = k(4x)² = 16kx². New values: kx² + k(3x)² = kx² + 9kx² = 10kx². Loss = 16kx² - 10kx² = 6kx². Loss percentage = (6/16) × 100 = 37.5%. The answer D (37.5%) is correct.

Multiple choice

One year ago the ratio between Mayank’s and Suresh’s salary was 3 : 4. The ratios of their individual salaries between last year’s and this year’s salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs. 4160. The salary of Mayank, now is?

  1. 1600 Rs

  2. 2560 Rs

  3. 1820 Rs

  4. 2400 Rs

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

One year ago, Mayank:Suresh = 3:4. Let their salaries be 3x and 4x. With increases 4:5 and 2:3, present salaries are (15x/4) and (6x/1) respectively. Sum = 16x = 4160, so x = 260. Mayank's present salary = 15 × 260 = 1600.