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

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%.

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).

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).

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%.

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%.

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%.

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

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%.

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%.

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).

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

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).

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).