Question 1:
A man sold a car at a 20% profit. If he had bought it for ₹10,000 less and sold it at the same selling price, his profit percentage would have been 50%. What was the original cost price of the car?
A) ₹40,000 B) ₹45,000 C) ₹50,000 D) ₹60,000 E) ₹65,000
Question 2:
A trader sells two cars for ₹40,000 each. On one he makes a 25% profit, and on the other he suffers a 25% loss. What is his overall profit or loss percentage?
A) 0% B) 3.25% profit C) 6.25% loss D) 12.5% loss E) 25% loss
Question 3:
A person sells two items for ₹2,400 each. On one he gains x%, and on the other he loses x%. What is the overall percentage gain or loss?
A) 2x% profit B) x²/100% loss C) x²/100% profit D) x/2% loss E) 0%
Question 4:
An article was sold for ₹1,200 at a loss of 20%. If it had been sold for ₹1,500, what would have been the profit or loss percent?
A) 0% B) 5% profit C) 10% profit D) 10% loss E) 20% profit
Question 5:
A man sells a bike at a 15% profit. If the cost price was ₹5,000 less and he sold it at the same selling price, what would be the new profit percentage?
A) 10% B) 20% C) 25% D) 30% E) Cannot be determined
answers and explanations
A1 C.
Explanation:
Let the original cost price be CP.
Given: He sold at a 20% profit, so
Selling Price (SP) = 1.20 × CP
If he had bought it for ₹10,000 less, his cost would have been CP – 10000 and he still sold it at the same SP.
In that case, profit % = 50% (from corrected version). So,
SP = 1.50 × (CP – 10000)
Equating the two SP expressions:1.20 × CP = 1.50 × (CP – 10000)
→ 1.20CP = 1.50CP – 15000
→ 1.50CP – 1.20CP = 15000
→ 0.30CP = 15000
→ CP = 15000 / 0.30 = ₹50,000
A2 C.
Explanation:
Two cars sold for ₹40,000 each.
Car 1: 25% profit → SP = ₹40,000
→ CP = 40000 / 1.25 = ₹32,000
Car 2: 25% loss → SP = ₹40,000
→ CP = 40000 / 0.75 = ₹53,333.33
Total CP = 32000 + 53333.33 = ₹85,333.33
Total SP = ₹80,000
Loss = 85333.33 – 80000 = ₹5333.33
Loss % = (5333.33 / 85333.33) × 100 ≈ 6.25%
Alternate shortcut: For equal SPs, gain x% on one and loss x% on other → net loss = x²/100 = 625/100 = 6.25%
A3 B.
Explanation:
This is the general identity:
If two items are sold at same SP, and one has a gain of x% and the other a loss of x%,
Net result = Loss = (x² / 100)%
So, answer is x²/100% loss, not dependent on actual SP values.
A4 A.
Explanation:
Sold at ₹1200 with 20% loss.
So, SP = 0.80 × CP → CP = 1200 / 0.80 = ₹1500
If sold at ₹1500, SP = CP → no profit, no loss
Profit % = 0%
A5 E.
Explanation:
Let original CP = C
Then SP = 1.15C
New CP = C – 5000
New profit % = ((SP – new CP) / new CP) × 100
= ((1.15C – (C – 5000)) / (C – 5000)) × 100
= ((0.15C + 5000) / (C – 5000)) × 100
Since C is not known, we cannot simplify to a numerical value.
Answer: Cannot be determined
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