Profit and Loss Concept and Questions solved For competitive Exams Wisdom Helps

Note: Formulas used are shown in brackets. (Profit% = (Profit/Cost Price)×100,
Loss% = (Loss/Cost Price)×100,  SP = CP×(1 ± percent/100))

For formulas and Concept, click here Profit and Loss Concept and Formulas 

Q1. A shopkeeper buys an article for ₹500 and sells it for ₹575. What is the profit percent?

A) 10%

B) 12.5%

C) 15%

D) 17.5%

Answer & Explanation

Correct Option: C) 15%
Steps: 1. Profit = SP − CP = 575 − 500 = ₹75.
2. Profit% = (Profit / CP) × 100 = (75 / 500) × 100 = 15%.

(Profit% = (Profit/CP)×100)

Shortcut: Profit 75 on 500 → 75/5 = 15%.

Q2. An item costing ₹1,200 is sold for ₹1,020. What is the loss percent?

A) 12%

B) 15%

C) 10%

D) 17.5%

Answer & Explanation

Correct Option: B) 15%
Steps: 1. Loss = CP − SP = 1200 − 1020 = ₹180.
2. Loss% = (Loss / CP) × 100 = (180 / 1200) × 100 = 15%.

(Loss% = (Loss/CP)×100)

Shortcut: 180 is 1/6 of 1200 → (1/6)×100 = 16.66… — careful: that's wrong approach; compute exact: 180/1200 = 0.15 → 15%.

Q3. An article is sold at a profit of 10% for ₹550. What was the cost price?

A) ₹500

B) ₹495

C) ₹525

D) ₹505

Answer & Explanation

Correct Option: A) ₹500
Steps: 1. SP = CP × (1 + 10/100) = CP × 1.10.
2. CP = SP / 1.10 = 550 / 1.1 = ₹500.

(SP = CP×(1+profit%/100) ⇒ CP = SP/(1+profit%/100))

Shortcut: Since 10% profit → SP is 110% of CP. 550 is 110% → 1% = 5 → 100% = 500.

Q4. An article costing ₹800 is sold at a loss of 12.5%. What is the selling price?

A) ₹700

B) ₹720

C) ₹680

D) ₹750

Answer & Explanation

Correct Option: A) ₹700
Steps: 1. Loss% = 12.5% = 1/8. SP = CP × (1 − 12.5/100) = CP × 0.875.
2. SP = 800 × 0.875 = 700.

(SP = CP×(1−loss%/100))

Shortcut: 12.5% of 800 = 100 → SP = 800 − 100 = 700.

Q5. A trader buys two identical shirts at ₹200 each. He sells one at 25% profit and the other at 10% loss. What is his overall gain or loss percent?

A) 7.5% profit

B) 5% profit

C) 2.5% loss

D) 10% profit

Answer & Explanation

Correct Option: A) 7.5% profit
Steps: 1. Total CP = 200 + 200 = 400.
2. SP1 = 200 × 1.25 = 250. SP2 = 200 × 0.90 = 180. Total SP = 430.
3. Profit = 430 − 400 = ₹30. Profit% = (30/400)×100 = 7.5%.

(TotalProfit% = (TotalSP−TotalCP)/TotalCP×100)

Shortcut: Average effect — compute totals; avoid averaging percent directly.

Q6. A shopkeeper marks an article at ₹1,200 (marked price). He gives a 25% discount and sells it. If cost price was ₹800, what is the profit percent?

A) 20%

B) 12.5%

C) 10%

D) 15%

Answer & Explanation

Correct Option: B) 12.5%
Steps: 1. Discount 25% on ₹1,200 → SP = 1200 × 0.75 = ₹900.
2. Profit = SP − CP = 900 − 800 = ₹100. Profit% = (100/800)×100 = 12.5%.

(SP = MP×(1−discount/100); Profit%=(Profit/CP)×100)

Shortcut: 25% off 1200 = 300 → SP = 900; compare with CP.

Q7. An article with cost price ₹1,500 is marked 10% above cost. Two successive discounts 10% and 20% are given on the marked price. What is the final result?

A) 6% profit

B) 4% loss

C) 2% profit

D) 8% loss

Answer & Explanation

Correct Option: B) 4% loss
Steps: 1. MP = CP × 1.10 = 1500 × 1.10 = 1650.
2. Successive discounts: overall factor = 0.90 × 0.80 = 0.72. SP = 1650 × 0.72 = 1188.
3. Loss = 1500 − 1188 = ₹312. Loss% = (312/1500)×100 = 20.8% — WAIT this seems off; re-check calculation carefully.
Recompute carefully: MP = 1500 × 1.10 = 1650. SP = 1650 × 0.9 = 1485; then ×0.8 = 1188 (same). Loss = 1500 − 1188 = 312. Loss% = (312/1500)×100 = 20.8% — that is not in options. That means our initial option set assumed MP of 1500? To remain consistent, we must correct problem parameters so result matches a clean option.

Q7. An article has cost price ₹1,500. It is marked 20% above cost and then sold after two successive discounts of 10% and 20% on the marked price. What is the final profit or loss percent?

A) 4% loss

B) 6% profit

C) 2% loss

D) 8% profit

Answer & Explanation

Correct Option: A) 4% loss
Steps (careful arithmetic): 1. MP = CP × 1.20 = 1500 × 1.20 = 1800.
2. Successive discounts factor = 0.90 × 0.80 = 0.72. So SP = 1800 × 0.72 = 1296.
3. Loss = 1500 − 1296 = ₹204. Loss% = (204/1500)×100 = 13.6% — oh, that's not 4% either. Let's recompute with controlled numbers to produce a clean option. To avoid confusion, I'll swap to a simpler version below that gives a clean 4% loss.

Q7. An article with cost price ₹1,000 is marked 20% above cost. A single discount of 10% is given on the marked price. What is the seller's profit or loss percent?

A) 8% profit

B) 2% loss

C) 10% profit

D) 12% profit

Answer & Explanation

Correct Option: A) 8% profit
Steps: 1. MP = 1000 × 1.20 = 1200.
2. After 10% discount SP = 1200 × 0.90 = 1080.
3. Profit = 1080 − 1000 = ₹80. Profit% = (80/1000)×100 = 8%.

(MP = CP×(1+markup%); SP = MP×(1−discount%))

Shortcut: Mark-up 20% → +200 → MP 1200; 10% off → −120 → SP 1080.

Q8. If the profit on selling an article is 1/5 of the selling price, what is the profit percent (to nearest integer)?

A) 20%

B) 25%

C) 16.67%

D) 33.33%

Answer & Explanation

Correct Option: B) 25%
Steps: 1. Let SP = S. Profit = S/5. Then CP = SP − Profit = S − S/5 = 4S/5.
2. Profit% = (Profit / CP) × 100 = (S/5) / (4S/5) × 100 = (1/4)×100 = 25%.

(If Profit = k×SP, Profit% = k/(1−k) ×100)

Shortcut: Profit is 1/5 of SP → CP is 4/5 of SP → profit/CP = (1/5)/(4/5) = 1/4.

Q9. When an article is sold at 10% profit, and if it had been sold for ₹20 more it would have given 15% profit. What is the cost price?

A) ₹400

B) ₹500

C) ₹320

D) ₹200

Answer & Explanation

Correct Option: A) ₹400
Steps (algebra): 1. Let CP = x. SP1 (10% profit) = 1.10x. SP2 (15% profit) = 1.15x. Given SP2 = SP1 + 20 → 1.15x − 1.10x = 20.
2. 0.05x = 20 ⇒ x = 20 / 0.05 = 400.

(SP = CP×(1+profit%/100))

Shortcut: 5% of CP = ₹20 ⇒ CP = 20 × (100/5) = 400.

Q10. An article is sold at 3/4 of its cost price. What is the loss percent?

A) 25%

B) 20%

C) 33.33%

D) 15%

Answer & Explanation

Correct Option: A) 25%
Steps: 1. SP = (3/4)CP ⇒ Loss = CP − SP = CP − 3CP/4 = CP/4.
2. Loss% = (CP/4)/CP × 100 = 25%.

(If SP = k·CP, Loss% = (1−k)×100 if k<1 div=""> Shortcut: Sold at 75% of CP → loss = 25% of CP.

Q11. A trader marks goods 40% above cost and allows a 20% discount on the marked price. What is his overall profit percent?

A) 12%

B) 8%

C) 14%

D) 10%

Answer & Explanation

Correct Option: B) 8%
Steps: 1. Let CP = 100. MP = 100 × 1.40 = 140. After 20% discount SP = 140 × 0.80 = 112.
2. Profit = 112 − 100 = 12. Profit% = (12/100)×100 = 12% — wait that's 12%. But re-check: 140×0.8=112, profit 12 on 100 => 12%. My initial option list included 12% (A). Correct option is 12%.
Correction: Correct Option: A) 12%

(MP = CP×(1+markup%); SP = MP×(1−discount%))

Shortcut: (1 + 0.40)×(1 − 0.20) −1 = (1.4×0.8) −1 = 1.12 −1 = 0.12 → 12%.

Q12. Two articles cost ₹150 and ₹250 respectively. They are sold together for ₹460. What is the overall profit percent?

A) 15%

B) 10%

C) 12.5%

D) 8%

Answer & Explanation

Correct Option: A) 15%
Steps: 1. Total CP = 150 + 250 = 400. Total SP = 460.
2. Profit = 60. Profit% = (60/400)×100 = 15%.

(TotalProfit% = (TotalSP−TotalCP)/TotalCP×100)

Shortcut: Profit 60 on 400 → 60/4 = 15%.

Q13. A shopkeeper's profit percent becomes double when he increases the selling price by 20%. What was the original profit percent?

A) 25%

B) 20%

C) 15%

D) 30%

Answer & Explanation

Correct Option: A) 25%
Steps (algebra, careful): 1. Let CP = 1 (use relative CP). Let original profit% = p ⇒ original SP = 1 + p. (Here p in decimal: e.g., 25% ⇒ p=0.25)
2. After increasing SP by 20%: new SP = 1.20(1 + p). Given new profit = 2×original profit ⇒ new SP = 1 + 2p.
3. So 1.20(1 + p) = 1 + 2p → 1.20 + 1.20p = 1 + 2p → 0.20 = 0.80p → p = 0.25 = 25%.

(1.2(1+p)=1+2p ⇒ solve for p)

Shortcut: Translate percent to decimals and solve linear equation.

Q14. An article is marked at 25% above cost. It is sold at 10% discount on the marked price. What is the net profit percent?

A) 12.5%

B) 15%

C) 10%

D) 8%

Answer & Explanation

Correct Option: A) 12.5%
Steps: 1. Let CP = 100. MP = 125. After 10% discount SP = 125 × 0.90 = 112.5.
2. Profit = 112.5 − 100 = 12.5. Profit% = 12.5%.

(Net factor = (1+markup%)×(1−discount%)−1)

Shortcut: (1.25×0.9) = 1.125 → 12.5% profit.

Q15. Two identical items are bought for ₹100 each. One is sold at 30% profit and the other at 20% loss. What is the overall percent result?

A) 5% profit

B) 2.5% profit

C) 0% (break-even)

D) 10% loss

Answer & Explanation

Correct Option: A) 5% profit
Steps: 1. CP total = 100 + 100 = 200. SP1 = 100 × 1.30 = 130. SP2 = 100 × 0.80 = 80. Total SP = 210.
2. Profit = 10 on 200 → (10/200)×100 = 5%.

(TotalProfit% = (TotalSP−TotalCP)/TotalCP×100)

Shortcut: Pairwise compute totals; avoid averaging percentages.

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