Percentage & Fraction Questions (11–20)

Q11: A's income is 60% of B's and B's income is 80% of C's. What % of C's income is A's?

A = 60% of B = 60% of (80% of C) = 0.6 × 0.8 = 0.48
So A = 48% of C

Q12: In a test, 80% passed in Maths, 85% in English, 75% in both. What % failed in both?

% passed in at least one = 80 + 85 – 75 = 90%
So, failed in both = 100 – 90 = 10%

Q13: A spends 80% of income. Income ↑ 20%, expenses ↑ 10%. Find % increase in savings.

Let income = 100, expenses = 80, savings = 20
New income = 120, new expenses = 88
New savings = 32 → % increase = (12/20)×100 = 60%

Q14: A is 20% more efficient than B. A completes work in 12 days. Find B’s time.

A : B efficiency = 120 : 100 = 6 : 5 → Time = 5 : 6
B’s time = 12 × 6 / 5 = 14.4 days

Q15: A reduction of 20% in price allows a person to buy 25% more. Find % change in expenditure.

Let price = ₹100, quantity = 1 unit → expense = ₹100
New price = ₹80, quantity = 1.25 units → expense = ₹100
No change in expenditure

Q16: A’s salary is increased by 10% and then decreased by 10%. What's the net effect?

Net % change = –(10 × 10)/100 = –1%
1% decrease

Q17: A fruit seller makes a loss of 10% after giving 20% extra. What is the profit % if no extra is given?

S.P. for 1.2 kg = 0.9 → SP per kg = 0.75
Now sells at 1 kg = 1 → profit = (1 – 0.75)/0.75 = 33.33%

Q18: In an election, one got 56% valid votes. 20% invalid. Total = 10,000. Find margin.

Valid votes = 8000 → 56% = 4480, opponent = 3520
Margin = 4480 – 3520 = 960 votes

Q19: A’s income 25% more than B, and B’s 20% less than C. A is what % of C?

Let C = 100 → B = 80 → A = 1.25 × 80 = 100%

Q20: Price ↓ 10%, quantity ↑ 10%. What is % change in expenditure?

Change = 0.9 × 1.1 = 0.99 → 1% decrease

RDFC