Ratio with Percentage MCQ Quiz - Objective Question with Answer for Ratio with Percentage - Download Free PDF

Last updated on May 9, 2025

Latest Ratio with Percentage MCQ Objective Questions

Ratio with Percentage Question 1:

The ratio between the number of males and females in a college is 21 ∶ 22. If the number of males is increased by 20% and the number of females is increased by 30%, then what will be the new ratio of males and females in the college?

  1. 127 : 143
  2. 125 : 143
  3. 128 : 143
  4. 126 : 143

Answer (Detailed Solution Below)

Option 4 : 126 : 143

Ratio with Percentage Question 1 Detailed Solution

Given:

Male : Female = 21 : 22

Calculation:

New ratio of male to female = 21 × (100 + 20)% : 22 × (100 + 30)%

⇒ 21 × 120% : 22 × 130%

⇒ 21 × 12 : 22 × 13

⇒ 21 × 6 : 11 × 13

⇒ 126 : 143

∴ The new ratio of males and females in the college is 126 : 143

Ratio with Percentage Question 2:

The ratio of savings to expenditure of a woman is 2 ∶ 1. If her income and expenditure increase by 17% and 13% respectively, find the percentage increase in her savings.

  1. 26%
  2. 28%
  3. 27%
  4. 19%

Answer (Detailed Solution Below)

Option 4 : 19%

Ratio with Percentage Question 2 Detailed Solution

Given:

The ratio of savings to expenditure of a woman is 2 ∶ 1.

Income increase = 17%

Expenditure increase = 13%

Formula Used:

Savings = Income - Expenditure

Calculations:

Let the original savings be 2x and the original expenditure be x.

Therefore, the original income = savings + expenditure = 2x + x = 3x.

New income = 3x × 1.17 = 3.51x

New expenditure = x × 1.13 = 1.13x

New savings = New income - New expenditure = 3.51x - 1.13x = 2.38x

Percentage increase in savings = (New savings - Original savings) / Original savings × 100

Percentage increase in savings = (2.38x - 2x) / 2x × 100 = 0.38x / 2x × 100 = 19%

∴ The percentage increase in her savings is 19%.

Ratio with Percentage Question 3:

Income of A is 30% more than that of B, and the savings of A and B are in the ratio of 3 : 2. If each of them spent ₹3,500, find the sum of incomes of A and B.

  1. ₹20,300
  2. ₹20,200
  3. ₹20,000
  4. ₹20,125

Answer (Detailed Solution Below)

Option 4 : ₹20,125

Ratio with Percentage Question 3 Detailed Solution

Given:

Income of A is 30% more than that of B

Savings of A and B are in the ratio of 3:2

Each of them spent ₹3,500

Formula used:

Savings = Income - Expenditure

Calculation:

If Income of B = ₹x, then Income of A = ₹1.3x

Savings of B = x - 3,500

Savings of A = 1.3x - 3,500

According to the given ratio:

(1.3x - 3,500) / (x - 3,500) = 3 / 2

⇒ 2(1.3x - 3,500) = 3(x - 3,500)

⇒ 2.6x - 7,000 = 3x - 10,500

⇒ 0.4x = 3,500

⇒ x = ₹8,750

Income of B = ₹8,750

Income of A = 1.3 x 8,750 = ₹11,375

Sum of incomes of A and B = ₹8,750 + ₹11,375 = ₹20,125

∴ The correct answer is option (4).

Ratio with Percentage Question 4:

The number of seats in an institute for class 10th, 11th and 12th are in the ratio 5 ∶ 7 ∶ 8. It is proposed to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

  1. 2 ∶ 3 ∶ 4
  2. 4 ∶ 5 ∶ 6
  3. 3 ∶ 4 ∶ 6
  4. 5 ∶ 6 ∶ 7

Answer (Detailed Solution Below)

Option 1 : 2 ∶ 3 ∶ 4

Ratio with Percentage Question 4 Detailed Solution

Given:

The number of seats in class 10th, 11th, and 12th are in the ratio 5:7:8.

Formula used:

Increased seats = Original seats × (1 + Percentage Increase/100)

Calculations:

Let the original seats be 5x, 7x, and 8x for classes 10th, 11th, and 12th respectively.

Increased seats for:

Class 10th: \((5x \times (1+\frac{40}{100}))\) = 7x

Class 11th: \((7x \times (1+\frac{50}{100}))\) = 10.5x

Class 12th: \((8x \times (1+\frac{75}{100}))\) = 14x

New Ratio of increased seats:

\((7x : 10.5x : 14x)\)

\((2 : 3 : 4)\)

∴ The correct answer is option (1).

Ratio with Percentage Question 5:

The ratio of expenditure to savings of a woman is 5 ∶ 1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.

  1. 55%
  2. 60%
  3. 50%
  4. 40%

Answer (Detailed Solution Below)

Option 4 : 40%

Ratio with Percentage Question 5 Detailed Solution

Given:

The ratio of expenditure to savings of a woman is 5 ∶ 1. 

Her income and expenditure are increased by 10% and 20% respectively.

Concept used:

1. Income = Expenditure + Savings

2. Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let her initial expenditure and savings be 5k and k respectively.

Her initial income = 5k + k = 6k

Her final income = 6k × (1 + 10%) = 6.6k

Her final expenditure = 5k × (1 + 20%) = 6k

Her final savings = 6.6k - 6k = 0.6k

Now, % change in savings = \(\frac {k - 0.6k}{k} × 100\%\) = 40%

∴ The percentage change in her savings is 40%.

Shortcut TrickCalculation:

Income = expenditure + saving

⇒ (6 = 5 + 1) × 100

⇒ 600 = 500 + 100

Now, income is increased by 10% and expenditure is increased by 20%.

⇒ 600 × 110% = 500 × 120% + x

⇒ 660 = 600 + x

⇒ x = 60

Percentage change in saving = (100 - 60)/100 = 40%

∴ The correct answer is 40%.

Top Ratio with Percentage MCQ Objective Questions

The ratio of expenditure to savings of a woman is 5 ∶ 1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.

  1. 55%
  2. 60%
  3. 50%
  4. 40%

Answer (Detailed Solution Below)

Option 4 : 40%

Ratio with Percentage Question 6 Detailed Solution

Download Solution PDF

Given:

The ratio of expenditure to savings of a woman is 5 ∶ 1. 

Her income and expenditure are increased by 10% and 20% respectively.

Concept used:

1. Income = Expenditure + Savings

2. Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let her initial expenditure and savings be 5k and k respectively.

Her initial income = 5k + k = 6k

Her final income = 6k × (1 + 10%) = 6.6k

Her final expenditure = 5k × (1 + 20%) = 6k

Her final savings = 6.6k - 6k = 0.6k

Now, % change in savings = \(\frac {k - 0.6k}{k} × 100\%\) = 40%

∴ The percentage change in her savings is 40%.

Shortcut TrickCalculation:

Income = expenditure + saving

⇒ (6 = 5 + 1) × 100

⇒ 600 = 500 + 100

Now, income is increased by 10% and expenditure is increased by 20%.

⇒ 600 × 110% = 500 × 120% + x

⇒ 660 = 600 + x

⇒ x = 60

Percentage change in saving = (100 - 60)/100 = 40%

∴ The correct answer is 40%.

The ratio of savings to expenditure of a woman is 2 ∶ 1. If her income and expenditure increase by 17% and 13% respectively, find the percentage increase in her savings.

  1. 26%
  2. 28%
  3. 27%
  4. 19%

Answer (Detailed Solution Below)

Option 4 : 19%

Ratio with Percentage Question 7 Detailed Solution

Download Solution PDF

Given:

The ratio of savings to expenditure of a woman is 2 ∶ 1.

Income increase = 17%

Expenditure increase = 13%

Formula Used:

Savings = Income - Expenditure

Calculations:

Let the original savings be 2x and the original expenditure be x.

Therefore, the original income = savings + expenditure = 2x + x = 3x.

New income = 3x × 1.17 = 3.51x

New expenditure = x × 1.13 = 1.13x

New savings = New income - New expenditure = 3.51x - 1.13x = 2.38x

Percentage increase in savings = (New savings - Original savings) / Original savings × 100

Percentage increase in savings = (2.38x - 2x) / 2x × 100 = 0.38x / 2x × 100 = 19%

∴ The percentage increase in her savings is 19%.

The ratio between the number of males and females in a college is 21 ∶ 22. If the number of males is increased by 20% and the number of females is increased by 30%, then what will be the new ratio of males and females in the college?

  1. 127 : 143
  2. 125 : 143
  3. 128 : 143
  4. 126 : 143

Answer (Detailed Solution Below)

Option 4 : 126 : 143

Ratio with Percentage Question 8 Detailed Solution

Download Solution PDF

Given:

Male : Female = 21 : 22

Calculation:

New ratio of male to female = 21 × (100 + 20)% : 22 × (100 + 30)%

⇒ 21 × 120% : 22 × 130%

⇒ 21 × 12 : 22 × 13

⇒ 21 × 6 : 11 × 13

⇒ 126 : 143

∴ The new ratio of males and females in the college is 126 : 143

Ratio with Percentage Question 9:

The ratio of expenditure to savings of a woman is 5 ∶ 1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.

  1. 55%
  2. 60%
  3. 50%
  4. 40%

Answer (Detailed Solution Below)

Option 4 : 40%

Ratio with Percentage Question 9 Detailed Solution

Given:

The ratio of expenditure to savings of a woman is 5 ∶ 1. 

Her income and expenditure are increased by 10% and 20% respectively.

Concept used:

1. Income = Expenditure + Savings

2. Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let her initial expenditure and savings be 5k and k respectively.

Her initial income = 5k + k = 6k

Her final income = 6k × (1 + 10%) = 6.6k

Her final expenditure = 5k × (1 + 20%) = 6k

Her final savings = 6.6k - 6k = 0.6k

Now, % change in savings = \(\frac {k - 0.6k}{k} × 100\%\) = 40%

∴ The percentage change in her savings is 40%.

Shortcut TrickCalculation:

Income = expenditure + saving

⇒ (6 = 5 + 1) × 100

⇒ 600 = 500 + 100

Now, income is increased by 10% and expenditure is increased by 20%.

⇒ 600 × 110% = 500 × 120% + x

⇒ 660 = 600 + x

⇒ x = 60

Percentage change in saving = (100 - 60)/100 = 40%

∴ The correct answer is 40%.

Ratio with Percentage Question 10:

The ratio of savings to expenditure of a woman is 2 ∶ 1. If her income and expenditure increase by 17% and 13% respectively, find the percentage increase in her savings.

  1. 26%
  2. 28%
  3. 27%
  4. 19%

Answer (Detailed Solution Below)

Option 4 : 19%

Ratio with Percentage Question 10 Detailed Solution

Given:

The ratio of savings to expenditure of a woman is 2 ∶ 1.

Income increase = 17%

Expenditure increase = 13%

Formula Used:

Savings = Income - Expenditure

Calculations:

Let the original savings be 2x and the original expenditure be x.

Therefore, the original income = savings + expenditure = 2x + x = 3x.

New income = 3x × 1.17 = 3.51x

New expenditure = x × 1.13 = 1.13x

New savings = New income - New expenditure = 3.51x - 1.13x = 2.38x

Percentage increase in savings = (New savings - Original savings) / Original savings × 100

Percentage increase in savings = (2.38x - 2x) / 2x × 100 = 0.38x / 2x × 100 = 19%

∴ The percentage increase in her savings is 19%.

Ratio with Percentage Question 11:

Income of A is 30% more than that of B, and the savings of A and B are in the ratio of 3 : 2. If each of them spent ₹3,500, find the sum of incomes of A and B.

  1. ₹20,300
  2. ₹20,200
  3. ₹20,000
  4. ₹20,125

Answer (Detailed Solution Below)

Option 4 : ₹20,125

Ratio with Percentage Question 11 Detailed Solution

Given:

Income of A is 30% more than that of B

Savings of A and B are in the ratio of 3:2

Each of them spent ₹3,500

Formula used:

Savings = Income - Expenditure

Calculation:

If Income of B = ₹x, then Income of A = ₹1.3x

Savings of B = x - 3,500

Savings of A = 1.3x - 3,500

According to the given ratio:

(1.3x - 3,500) / (x - 3,500) = 3 / 2

⇒ 2(1.3x - 3,500) = 3(x - 3,500)

⇒ 2.6x - 7,000 = 3x - 10,500

⇒ 0.4x = 3,500

⇒ x = ₹8,750

Income of B = ₹8,750

Income of A = 1.3 x 8,750 = ₹11,375

Sum of incomes of A and B = ₹8,750 + ₹11,375 = ₹20,125

∴ The correct answer is option (4).

Ratio with Percentage Question 12:

The ratio between the number of males and females in a college is 21 ∶ 22. If the number of males is increased by 20% and the number of females is increased by 30%, then what will be the new ratio of males and females in the college?

  1. 127 : 143
  2. 125 : 143
  3. 128 : 143
  4. 126 : 143

Answer (Detailed Solution Below)

Option 4 : 126 : 143

Ratio with Percentage Question 12 Detailed Solution

Given:

Male : Female = 21 : 22

Calculation:

New ratio of male to female = 21 × (100 + 20)% : 22 × (100 + 30)%

⇒ 21 × 120% : 22 × 130%

⇒ 21 × 12 : 22 × 13

⇒ 21 × 6 : 11 × 13

⇒ 126 : 143

∴ The new ratio of males and females in the college is 126 : 143

Ratio with Percentage Question 13:

If 10% of (a + b) = 50% of (a - b), then a ∶ b is:

  1. 5 ∶ 2
  2. 2 ∶ 3
  3. 3 ∶ 2
  4. 1 ∶ 2

Answer (Detailed Solution Below)

Option 3 : 3 ∶ 2

Ratio with Percentage Question 13 Detailed Solution

Given:

10% of (a + b) = 50% of (a - b)

Calculation:

⇒ 0.1 × (a + b) = 0.5 × (a - b)

⇒ 0.1a + 0.1b = 0.5a - 0.5b

⇒ 0.1b + 0.5b = 0.5a - 0.1a

⇒ 0.6b = 0.4a

\(\frac{a}{b} = \frac{0.6}{0.4}\)

\(\frac{a}{b} = \frac{3}{2}\)

The correct answer is option (3).

Ratio with Percentage Question 14:

The number of seats in an institute for class 10th, 11th and 12th are in the ratio 5 ∶ 7 ∶ 8. It is proposed to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

  1. 2 ∶ 3 ∶ 4
  2. 4 ∶ 5 ∶ 6
  3. 3 ∶ 4 ∶ 6
  4. 5 ∶ 6 ∶ 7

Answer (Detailed Solution Below)

Option 1 : 2 ∶ 3 ∶ 4

Ratio with Percentage Question 14 Detailed Solution

Given:

The number of seats in class 10th, 11th, and 12th are in the ratio 5:7:8.

Formula used:

Increased seats = Original seats × (1 + Percentage Increase/100)

Calculations:

Let the original seats be 5x, 7x, and 8x for classes 10th, 11th, and 12th respectively.

Increased seats for:

Class 10th: \((5x \times (1+\frac{40}{100}))\) = 7x

Class 11th: \((7x \times (1+\frac{50}{100}))\) = 10.5x

Class 12th: \((8x \times (1+\frac{75}{100}))\) = 14x

New Ratio of increased seats:

\((7x : 10.5x : 14x)\)

\((2 : 3 : 4)\)

∴ The correct answer is option (1).

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