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?
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
Ratio with Percentage Question 6 Detailed Solution
Download Solution PDFGiven:
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.
Answer (Detailed Solution Below)
Ratio with Percentage Question 7 Detailed Solution
Download Solution PDFGiven:
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?
Answer (Detailed Solution Below)
Ratio with Percentage Question 8 Detailed Solution
Download Solution PDFGiven:
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.
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
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:
Answer (Detailed Solution Below)
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?
Answer (Detailed Solution Below)
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).