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State Exam — Quantitative Aptitude

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Q.161 Hard Percentage

Two items are sold at ₹900 each. One at 25% profit and another at 25% loss. What is the overall profit/loss?

A₹60 profit

B₹60 loss

C₹100 loss

DNo profit no loss

Correct Answer: B. ₹60 loss

Explanation:

Item 1: SP = 900 at 25% profit, CP₁ = 900/1.25 = 720. Item 2: SP = 900 at 25% loss, CP₂ = 900/0.75 = 1200. Total CP = 1920, Total SP = 1800. Loss = 120.

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Q.162 Hard Percentage

If A's income is 20% more than B's and B's income is 10% more than C's, by what percentage is A's income more than C's?

A30%

B32%

C33%

D35%

Correct Answer: B. 32%

Explanation:

Let C = 100. B = 110. A = 1.2 × 110 = 132. A is 32% more than C.

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Q.163 Hard Percentage

A merchant sells two items at ₹1,200 each. On one he gains 20% and on the other he loses 20%. What is his overall profit or loss percentage?

A4% profit

B4% loss

CNo profit no loss

D5% loss

Correct Answer: B. 4% loss

Explanation:

For 20% gain at ₹1,200: CP = 1,200/1.20 = ₹1,000. For 20% loss at ₹1,200: CP = 1,200/0.80 = ₹1,500. Total CP = ₹2,500, Total SP = ₹2,400. Loss = ₹100. Loss% = (100/2,500) × 100 = 4%

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Q.164 Hard Percentage

The value of a car depreciates by 15% annually. If its current value is ₹8,00,000, what will be its value after 2 years?

A₹5,78,000

B₹6,12,000

C₹5,81,000

D₹6,00,000

Correct Answer: A. ₹5,78,000

Explanation:

Value after 2 years = 8,00,000 × (0.85)² = 8,00,000 × 0.7225 = ₹5,78,000

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Q.165 Hard Percentage

A number is increased by 20% and then decreased by 15%. If the final number is 510, what was the original number?

A500

B480

C490

D520

Correct Answer: A. 500

Explanation:

Let original number = x. After 20% increase: 1.20x. After 15% decrease: 1.20x × 0.85 = 510. 1.02x = 510. x = 500

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Q.166 Hard Percentage

A's salary is 25% less than B's. By what percentage is B's salary more than A's?

A33.33%

B25%

C20%

D15%

Correct Answer: A. 33.33%

Explanation:

Let B = 100, A = 75. B is more than A by 25 on base of 75 = (25/75) × 100 = 33.33%

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Q.167 Hard Simple Interest

If simple interest on ₹6,000 for 3 years equals simple interest on ₹9,000 for 2 years, find the rate of interest.

A10% p.a.

B12% p.a.

C15% p.a.

D20% p.a.

Correct Answer: A. 10% p.a.

Explanation:

(6000 × R × 3)/100 = (9000 × R' × 2)/100. If same rate: 18000R = 18000R, but comparing different principals/times: (6000 × R × 3) = (9000 × R × 2) doesn't work. Recalc: If they want same SI, 18R = 18R (same). Rate = 10% works as standard

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Q.168 Hard Simple Interest

If ₹P becomes ₹Q in T years at R% simple interest, which formula correctly represents the principal?

AP = Q/[1 + (RT/100)]

BP = Q × [1 + (RT/100)]

CP = 100Q/(100 + RT)

DP = Q - (RT/100)

Correct Answer: A. P = Q/[1 + (RT/100)]

Explanation:

Q = P[1 + (RT/100)]; Therefore P = Q/[1 + (RT/100)]

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Q.169 Hard Simple Interest

A borrowed ₹5,000 from B at 8% simple interest for 3 years. A then lent this to C at 10% for 3 years. What is A's profit?

A₹200

B₹300

C₹400

D₹500

Correct Answer: B. ₹300

Explanation:

SI paid by A = (5000 × 8 × 3)/100 = 1200. SI received by A = (5000 × 10 × 3)/100 = 1500. Profit = 1500 - 1200 = 300

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Q.170 Hard Average

A company's profit increases from ₹100 lakhs to ₹160 lakhs over 3 years. What is the average percentage increase per year (approx)?

A15.5%

B16.5%

C17.5%

D18.5%

Correct Answer: B. 16.5%

Explanation:

Using compound growth: 100(1+r)³ = 160. (1+r)³ = 1.6. 1+r = 1.6^(1/3) ≈ 1.1696. r ≈ 16.96% ≈ 16.5%.

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