Direct or Indirect Proportion MCQ Quiz - Objective Question with Answer for Direct or Indirect Proportion - Download Free PDF

Last updated on Jun 5, 2025

Testbook brings a selection of Direct or Indirect Proportion MCQs for our candidates to have the best practice material. Solve these questions and boost your scores in exams like UPSC, MTS, SSC CGL, Bank Exams, etc. with this Direct and Indirect Proportion Quiz prepared by Testbook. In a direct proportion, the ratio between matching quantities stays the same if they are divided. (They form equivalent fractions). In an indirect (or inverse) proportion, as one quantity increases, the other decreases. It is an easy concept but can cause simple mistakes. Practice it with Testbook’s Direct and Indirect Proportion Quiz and avoid mistakes. Get several tips and tricks that will help you solve the Direct or Indirect Proportion Objective Questions quickly and relatively easily. There is no alternative to practice in the discipline of Quant and hence we have made efforts to make this process as easy for you as possible.

Latest Direct or Indirect Proportion MCQ Objective Questions

Direct or Indirect Proportion Question 1:

Salaries of Rahim and Karim are in the ratio 2 : 3. If the salary of each is increased by ₹2000, the new ratio becomes 40 : 57. What is Karim's present salary? a) 

  1. ₹25800
  2. ₹17000
  3. ₹14600
  4. ₹20000

Answer (Detailed Solution Below)

Option 2 : ₹17000

Direct or Indirect Proportion Question 1 Detailed Solution

Given:

Salaries of Rahim and Karim are in the ratio 2:3.

Salary of each is increased by ₹2000, and the new ratio becomes 40:57.

Formula Used:

New Ratio = (Old Salary + Increment) / (Old Salary + Increment)

Calculation:

Let Rahim's present salary be 2x and Karim's present salary be 3x.

After increasing ₹2000, their salaries become:

Rahim: 2x + 2000

Karim: 3x + 2000

New ratio = 40:57

So, (2x + 2000) / (3x + 2000) = 40 / 57

Cross multiply:

57 × (2x + 2000) = 40 × (3x + 2000)

⇒ 114x + 114000 = 120x + 80000

⇒ 120x - 114x = 114000 - 80000

⇒ 6x = 34000

⇒ x = 34000 / 6 = 5666.67

Karim's present salary:

3x = 3 × 5666.67 = ₹17000

∴ Karim's present salary is ₹17000

Direct or Indirect Proportion Question 2:

E is 25% greater than B. The ratio of the A and B is 5:7 and D is 18 greater than C which is 60% of A. The ratio of C and D is 4:7. What is the value of E?

Given below are steps involved in the solution. Arrange them in sequential order. 

(A) C = 4 × 6 = 24

(B) B = (7/5) × 40 = 56

(C) Let C and D be 4k and 7k respectively

(D) E = (125/100) × 56 = 70

(E) D - C = 18 => 7k - 4k = 18 => k = 6

(F) A = (100/60) × 24 = 40

  1. CEAFBD
  2. CAFEDB 
  3. EFACDB
  4. CFEADB

Answer (Detailed Solution Below)

Option 1 : CEAFBD

Direct or Indirect Proportion Question 2 Detailed Solution

Given:

E is 25% greater than B.

A : B = 5 : 7

D is 18 greater than C.

C = 60% of A

C : D = 4 : 7

Formula Used:

Percentage increase: New Value = Original Value × (1 + Percentage/100)

Calculations:

Sequential order of steps: C, E, A, B, F, D

(C) Let C and D be 4k and 7k respectively

(E) D - C = 18 ⇒ 7k - 4k = 18 ⇒ 3k = 18 ⇒ k = 6

(A) C = 4 × 6 = 24

(F) A = (100/60) × 24 = 40

(B) B = (7/5) × 40 = 56

(D) E = (125/100) × 56 = 1.25 × 56 = 70

The correct sequence is: CEAFBD.

Direct or Indirect Proportion Question 3:

If 64 : x :: x : 169, and x > 0, find the value of x.

  1. 104
  2. 112
  3. 96
  4. 108

Answer (Detailed Solution Below)

Option 1 : 104

Direct or Indirect Proportion Question 3 Detailed Solution

Given:

64 : x :: x : 169

Formula used:

a : b :: c : d means a \times d = b \times c

Calculation:

64 : x :: x : 169

⇒ \(64 \times 169 = x \times x\)

⇒ \(64 \times 169 = x^2\)

⇒ \(x^2 = 64 \times 13^2\)

⇒ \(x^2 = (8 \times 13)^2\)

⇒ x = 104

∴ The correct answer is option 1.

Direct or Indirect Proportion Question 4:

If 9 : 12 :: 12 : k, then find the value of k + 1.  

  1. 18
  2. 15
  3. 16
  4. 17

Answer (Detailed Solution Below)

Option 4 : 17

Direct or Indirect Proportion Question 4 Detailed Solution

Given:

9 : 12 :: 12 : k

Formula used:

a : b :: c : d ⇒ b/a = d/c

Calculation:

12/9 = k/12

⇒ k = (12 × 12)/9

⇒ k = 16

⇒ So, k + 1 = 16 + 1

⇒ k + 1 = 17

∴ The correct answer is option (4).

Direct or Indirect Proportion Question 5:

If 12, 24, 45 and y are in proportion, then the value of y is:

  1. 60
  2. 25
  3. 90
  4. 30

Answer (Detailed Solution Below)

Option 3 : 90

Direct or Indirect Proportion Question 5 Detailed Solution

Given:

If 12, 24, 45 and y are in proportion, then the value of y is:

Formula used:

If a, b, c, d are in proportion, then a/b = c/d

Calculation:

12/24 = 45/y

⇒ 12 × y = 24 × 45

⇒ y = 1080/12

⇒ y = 90

∴ The correct answer is option (3).

Top Direct or Indirect Proportion MCQ Objective Questions

Gold is 12 times as heavy as aluminum and copper is 5 times as heavy as aluminum.In what ratio gold and copper should be mixed to get an alloy 8 times of aluminum.

  1. 2 : 1
  2. 3 : 4
  3. 1 : 2
  4. 4 : 3

Answer (Detailed Solution Below)

Option 2 : 3 : 4

Direct or Indirect Proportion Question 6 Detailed Solution

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Given:

Gold is 12 times as heavy as aluminum and copper  is 5 times as heavy as aluminum.

Calculation:

Let the ratio of gold and copper that taken be x : y

According to the question,

⇒ \(\frac{{12x + 5y}}{{x + y}} = \frac{8}{1}\)

⇒ 12x + 5y = 8x + 8y

⇒ 4x = 3y

⇒ x/y = 3/4

∴ Gold and copper are taken in the ratio 3 : 4.  Alternate Method

Allegation method use in this question,

F1 SSC  Priya 8 5 24 D3

∴ Gold and copper are taken in the ratio 3 : 4. 

If \(\frac{1}{a}:\frac{1}{7} = \frac{1}{{3.43}}:\frac{1}{a}\), then what is the value of a?

  1. 6.5
  2. 5.6
  3. 4.9
  4. 7.7

Answer (Detailed Solution Below)

Option 3 : 4.9

Direct or Indirect Proportion Question 7 Detailed Solution

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Given:

\(\frac{1}{a}:\frac{1}{7} = \frac{1}{{3.43}}:\frac{1}{a}\)

Calculation:

\(\frac{1}{a}:\frac{1}{7} = \frac{1}{{3.43}}:\frac{1}{a}\)

⇒ 7/a = a/3.43

⇒ a2 = 3.43 × 7

⇒ a = \(\sqrt {3.43 \times 7}\)

⇒ a = 4.9 (Considering the positive value only)

∴ The value of a is 4.9.

The ratio of the prices of tea to coffee is 3 ∶ 5 and the ratio of their quantities consumed by a family is 5  7. Find the ratio of expenditure on tea to coffee.

  1. 3
  2. 3 ∶ 7
  3. 3 ∶ 9
  4. 5 ∶ 3

Answer (Detailed Solution Below)

Option 2 : 3 ∶ 7

Direct or Indirect Proportion Question 8 Detailed Solution

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Given

ratio of the prices of tea to coffee is 3 ∶ 5

ratio of the quantities consumed by a family is 5  7

Formula used

expenditure =price \(\times\)quantities

Calculation

\(\frac{E1}{E2}=\frac{P1}{P2}\times \frac{Q1}{Q2}\)

\(\frac{E1}{E2}=\frac{3}{5}\times \frac{5}{7}=\frac{3}{7}\)

The ratio of the expenditure is 3:7

If (a3 + b3) is proportional to (a2 – b2), then (a2 - ab + b2) is proportional to

  1. (a - b)
  2. (a + b)
  3. (a + ab + b)
  4. (a3 – b3)

Answer (Detailed Solution Below)

Option 1 : (a - b)

Direct or Indirect Proportion Question 9 Detailed Solution

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Formula used:

a3 b= (a + b)(a- ab + b2)

a2 - b= (a + b)(a - b)

Calculation:

According to the question

(a3 + b3) ∝ (a2 – b2)

Using the above identities

⇒ (a + b)(a - ab + b2) ∝ (a + b)(a - b)

⇒ (a - ab + b2) ∝ (a - b)

∴ (a - ab + b2) will be proportional to the  a - b   

The price of two articles are in the ratio of 5 : 6 respectively. The price of first article is increased by 30% and the price of second article is decreased by X%. If the new ratio is 13 : 11 respectively, then what is the value of X?

  1. 9.09
  2. 8.33
  3. 11.11
  4. 12.5

Answer (Detailed Solution Below)

Option 2 : 8.33

Direct or Indirect Proportion Question 10 Detailed Solution

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Given:

The price of two articles are in the ratio of 5 : 6 

The price of first article is increased by 30%

The price of second article is decreased by X%

So the Ratio becomes 13 : 11

Calculation:

Let the price of the articles initially be 50 and 60 respectively

The price of first article is increased by 30%

⇒ 50 + (30/100) × 50 = 65

The price of second article is decreased by X%

⇒ 60 - {(X/100) × 60} = 60 × (100 - X)/100

So the Ratio becomes 13 : 11

⇒ 65/{60× (100 - X)/100} = 13/11

⇒ 715 = 780 × (100 - X)/100

⇒ 71500 = 78000 - 780X

⇒ 780X = 6500

∴ X = 8.33

A varies directly as (B + 18) and A = 108 when B = 36. Find the value of A when B = 68. 

  1. 75
  2. 86
  3. 127
  4. 172

Answer (Detailed Solution Below)

Option 4 : 172

Direct or Indirect Proportion Question 11 Detailed Solution

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Given :

A = k(B + 18), A = 108, B = 36

Calculation : 

⇒ A = k(B + 18)

⇒ 108 = k(36 + 18)

⇒ k = 108/54 = 2

A = 2 × (68 + 18)

⇒ 2 × 86 = 172

∴ The correct answer is 172.

Ramesh invested a certain amount in share market and gold in the ratio of 6 : 7 respectively. At the end of the year, he earned a total profit of 30% on his investment. After one year he reinvested the amount including profit in the ratio of 4 : 5 in share market and gold. If the amount reinvested in gold was Rs. 94,500/-.What was the original amount invested in gold?

  1. Rs. 70,456
  2. Rs. 70,000
  3. Rs. 75,000
  4. Rs. 84,000
  5. None of these 

Answer (Detailed Solution Below)

Option 1 : Rs. 70,456

Direct or Indirect Proportion Question 12 Detailed Solution

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Given:

Ratio of amount invested in share market and gold is 6 : 7

Profit earned on the investment after one year is 30%

Ratio of amount reinvested in share market and gold is 4 : 5

Amount reinvested in gold is Rs. 94,500

Calculation:

Since the amount reinvested is in the ratio = 4 : 5

Then total amount reinvested,

⇒ (Amount of gold reinvested × total of ratio)/part of gold in ratio

⇒ (94,500 × 9)/5 = Rs. 1,70,100

Since there was a profit in this amount = 30%

So the Original amount,

⇒ (Total amount reinvested × 100)/130 = Rs. 130846

Original amount invested in gold,

⇒ (130846 × 7)/13

⇒ Rs. 70,455.53 ≈ Rs. 70,456

Original amount invested in gold is Rs. 70,456

A bag contains Rs. 1 and 50 paise coins and the ratio of their value is 30 : 11. The total number of coins are 520. Find the number of 50 paise coins?

  1. 210
  2. 220
  3. 200
  4. 400

Answer (Detailed Solution Below)

Option 2 : 220

Direct or Indirect Proportion Question 13 Detailed Solution

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Given

Bag contains Rs. 1, 50 paise, coins

The ratio of value is 30 : 11

The total no. of coins are 520

Concept used

Ratio concept used

Calculation

Value of Rs. 1 and 50 paise coins = 30 : 11

Number of coins = 30 : 22

⇒ 52 part = 520

⇒ 1p = 10

⇒ 22p = 10 × 22

⇒ 220

Alternate Method Sunny 28.7.21

Calculation:

Rs. 1 = 100 paise 

Let the total number of 100 paise coins be x

Then 50 paise coins are 520 – x

According to the question,

⇒ 100x/50(520 – x) = 30/11

⇒ 11 × 100x = 30 × 50(520 – x)

⇒ 1,100x = 7,80,000 – 1,500x

⇒ 2,600x = 7,80,000

⇒ x = 7,80,000/2,600

⇒ x = 300

50 paise coins,

⇒ 520 – 300 = 220

∴ 50 paise coins are 220.

An amount of Rs. 5,800 is divided into three parts in such a way that half of the first part, one-fifth of the second part, and three-eighth of the third part are equal. The value of the third part is:

  1. Rs. 1,500
  2. Rs. 1,200
  3. Rs. 1,400
  4. Rs. 1,600

Answer (Detailed Solution Below)

Option 4 : Rs. 1,600

Direct or Indirect Proportion Question 14 Detailed Solution

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Calculation:

Let the first part be "a", second part be "b" and third part be "c".

According to the question-

⇒ \(1\over2\) × a = \(1\over5\) × b = \(3\over8\) × c 

Let  \(1\over2\) × a = \(1\over5\) × b = \(3\over8\) × c = k

⇒ a = 2k

⇒ b = 5k

 c = \(8\over3\)k

⇒ 2k + 5k + \(8\over3\)k = Rs 5800

⇒ 29k = Rs 5800 × 3

⇒ k = Rs 600

Substituting the value of k in the equation of "c"-

⇒  \(3\over8\) × c = Rs 600

⇒ c = Rs 1600

∴ The value of third part is Rs 1600.

The ratio of the present salaries of Vinod and Manoj is 6 : 7. If both of them get their salaries increased by Rs. 16,000, then the ratio becomes 8 : 9. What is the present salary of Manoj?

  1. Rs. 48,000
  2. Rs. 72,000
  3. Rs. 56,000
  4. Rs. 64,000

Answer (Detailed Solution Below)

Option 3 : Rs. 56,000

Direct or Indirect Proportion Question 15 Detailed Solution

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Given,

The ratio of the present salaries of Vinod and Manoj is 6 : 7

If both of them get their salaries increased by Rs. 16,000, then the ratio becomes 8 : 9.

Calculation:

Let the present salaries of Vinod and Manoj be 6x and 7x respectively

According to the question

(6x + 16000) / (7x + 16000) = 8/9

⇒ 9 (6x + 16000) = 8 (7x + 16000)

⇒ 54x + 144000 = 56x + 128000

⇒ 56x – 54x = 144000 – 128000

⇒ 2x = 16000

⇒ x = 16000/2

⇒ x = 8000

∴ Present salary of Manoj = 7 × 8000 = Rs. 56,000.

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