Profit & Loss – Hard Level Questions – UGC NET Paper 1

Q1): An item costs ₹800 and transport expense is ₹40. It is marked 25% above cost price (₹800) and sold at 10% discount. Find profit percent on total cost.
A) 6.25%
B) 7.14%
C) 8.33%
D) 10%

Answer: B) 7.14%

Explanation (Line-by-Line):

  • Step 1: Total cost = 800 + 40 = 840
  • Step 2: MP = 800 × 1.25 = 1000, so SP = 1000 × 0.90 = 900
  • Step 3: Profit = 900 − 840 = 60
  • Step 4: Profit% = (60/840) × 100 = 7.14%
  • Final: Profit percent is 7.14%, so option B is correct.

Q2): Two items are sold at the same selling price ₹540 each. On one item there is 20% profit and on the other there is 10% loss. Find overall profit/loss percent.
A) 2.86% profit
B) 2.86% loss
C) 3.33% profit
D) No profit no loss

Answer: A) 2.86% profit

Explanation (Line-by-Line):

  • Step 1: CP₁ = 540/1.20 = 450 and CP₂ = 540/0.90 = 600
  • Step 2: Total CP = 450 + 600 = 1050
  • Step 3: Total SP = 540 + 540 = 1080, so Profit = 1080 − 1050 = 30
  • Step 4: Profit% = (30/1050) × 100 = 2.86%
  • Final: Overall result is 2.86% profit, so option A is correct.

Q3): Find the equivalent single discount for successive discounts of 10%, 15%, and 20%.
A) 38.2%
B) 38.8%
C) 39.5%
D) 40%

Answer: B) 38.8%

Explanation (Line-by-Line):

  • Step 1: Successive discount factor = 0.90 × 0.85 × 0.80
  • Step 2: Factor = 0.612
  • Step 3: Equivalent discount = 1 − 0.612 = 0.388
  • Step 4: Discount% = 0.388 × 100 = 38.8%
  • Final: Equivalent single discount is 38.8%, so option B is correct.

Q4): A dealer marks goods 25% above cost price per kg and gives 10% discount on marked price, but uses 800 g as 1 kg. Find his gain percent.
A) 35%
B) 40%
C) 40.625%
D) 45%

Answer: C) 40.625%

Explanation (Line-by-Line):

  • Step 1: Take CP per kg = 200 (assume for easy calculation)
  • Step 2: MP = 200 × 1.25 = 250, billed SP = 250 × 0.90 = 225
  • Step 3: Actual cost given = 0.8 kg × 200 = 160
  • Step 4: Gain% = ((225 − 160)/160) × 100 = 40.625%
  • Final: Gain percent is 40.625%, so option C is correct.

Q5): CP = ₹750. The shopkeeper wants 20% profit after giving successive discounts of 10% and 5% on MP. Find MP (approx).
A) ₹1020
B) ₹1053
C) ₹1080
D) ₹1100

Answer: B) ₹1053 (approx)

Explanation (Line-by-Line):

  • Step 1: Required SP = 750 × 1.20 = 900
  • Step 2: Successive discount factor = 0.90 × 0.95 = 0.855
  • Step 3: SP = MP × 0.855 ⇒ MP = 900/0.855 = 1052.63
  • Step 4: Approx MP ≈ ₹1053
  • Final: Closest option is ₹1053, so option B is correct.

Q6): A trader sells an item at 15% profit. If he had bought it 10% cheaper and sold it 10% dearer, what would be the new profit percent (approx)?
A) 37.5%
B) 40.56%
C) 42%
D) 45.5%

Answer: B) 40.56%

Explanation (Line-by-Line):

  • Step 1: Original SP = 1.15 × CP
  • Step 2: New CP = 0.90 × CP and New SP = 1.10 × (1.15 × CP)
  • Step 3: New SP/New CP = (1.15 × 1.10)/0.90 = 1.40556
  • Step 4: New profit% = (1.40556 − 1) × 100 = 40.56%
  • Final: New profit percent is about 40.56%, so option B is correct.

Q7): The selling price at 25% profit is ₹420 more than the selling price at 10% loss (same CP). Find CP.
A) ₹1000
B) ₹1100
C) ₹1200
D) ₹1400

Answer: C) ₹1200

Explanation (Line-by-Line):

  • Step 1: Let CP = x, then SP₁ (25% profit) = 1.25x and SP₂ (10% loss) = 0.90x
  • Step 2: Difference = 1.25x − 0.90x = 0.35x
  • Step 3: 0.35x = 420 ⇒ x = 420/0.35 = 1200
  • Step 4: CP = ₹1200
  • Final: Cost price is ₹1200, so option C is correct.

Q8): An item is marked 60% above CP. What discount percent should be given to earn exactly 20% profit?
A) 20%
B) 22%
C) 25%
D) 30%

Answer: C) 25%

Explanation (Line-by-Line):

  • Step 1: MP = 1.60 × CP and required SP = 1.20 × CP
  • Step 2: SP = MP × (1 − d) ⇒ 1.20CP = 1.60CP × (1 − d)
  • Step 3: (1 − d) = 1.20/1.60 = 0.75
  • Step 4: d = 1 − 0.75 = 0.25 = 25%
  • Final: Required discount is 25%, so option C is correct.

Q9): A trader buys 40 kg at ₹50/kg and 60 kg at ₹60/kg. He sells the whole 100 kg at ₹65/kg. Find profit percent (approx).
A) 14.29%
B) 15%
C) 16.07%
D) 18%

Answer: C) 16.07%

Explanation (Line-by-Line):

  • Step 1: Total CP = 40×50 + 60×60 = 2000 + 3600 = 5600
  • Step 2: Total SP = 100 × 65 = 6500
  • Step 3: Profit = 6500 − 5600 = 900
  • Step 4: Profit% = (900/5600) × 100 = 16.07%
  • Final: Profit percent is about 16.07%, so option C is correct.

Q10): A shopkeeper gives 10% discount and still earns 35% profit. If he gives only 5% discount (same MP and CP), what will be the new profit percent?
A) 40%
B) 42.5%
C) 45%
D) 47.5%

Answer: B) 42.5%

Explanation (Line-by-Line):

  • Step 1: Let CP = 100, then profit 35% ⇒ SP = 135
  • Step 2: 10% discount means SP = 0.90 MP ⇒ MP = 135/0.90 = 150
  • Step 3: With 5% discount, new SP = 0.95 × 150 = 142.5
  • Step 4: New profit% = (142.5 − 100)/100 × 100 = 42.5%
  • Final: New profit percent is 42.5%, so option B is correct.

Q11): An item is sold at 20% profit. If the selling price is reduced by ₹120, it becomes a 10% loss. Find CP.
A) ₹300
B) ₹360
C) ₹400
D) ₹480

Answer: C) ₹400

Explanation (Line-by-Line):

  • Step 1: Let CP = x, then SP₁ = 1.20x
  • Step 2: Reduced SP₂ = 1.20x − 120 and loss 10% ⇒ SP₂ = 0.90x
  • Step 3: 1.20x − 120 = 0.90x ⇒ 0.30x = 120 ⇒ x = 400
  • Step 4: CP = ₹400
  • Final: Cost price is ₹400, so option C is correct.

Q12): A shopkeeper marks an item 30% above CP and gives successive discounts of 10% and 10%. Find profit percent.
A) 3%
B) 5.3%
C) 7%
D) 10%

Answer: B) 5.3%

Explanation (Line-by-Line):

  • Step 1: Overall factor on CP = 1.30 × 0.90 × 0.90
  • Step 2: Factor = 1.053
  • Step 3: Profit factor 1.053 means profit = 0.053 of CP
  • Step 4: Profit% = 0.053 × 100 = 5.3%
  • Final: Profit percent is 5.3%, so option B is correct.

Q13): A trader gives 5% discount on the billed amount but uses 800 g as 1 kg. He charges the cost price per kg (before discount). Find gain percent.
A) 15%
B) 18.75%
C) 20%
D) 25%

Answer: B) 18.75%

Explanation (Line-by-Line):

  • Step 1: Effective collection factor due to discount = 0.95
  • Step 2: Effective quantity factor due to false weight = 1000/800 = 1.25
  • Step 3: Net gain factor = 0.95 × 1.25 = 1.1875
  • Step 4: Gain% = (1.1875 − 1) × 100 = 18.75%
  • Final: Gain percent is 18.75%, so option B is correct.

Q14): CP = ₹500 and expenses = 20% of CP. Item is marked 60% above CP. What discount percent gives 25% profit on total cost?
A) 5%
B) 6.25%
C) 7.5%
D) 8%

Answer: B) 6.25%

Explanation (Line-by-Line):

  • Step 1: Total cost = 500 + 20% of 500 = 500 + 100 = 600
  • Step 2: Required SP for 25% profit = 600 × 1.25 = 750
  • Step 3: MP = 500 × 1.60 = 800, so discount% = (800 − 750)/800 × 100
  • Step 4: Discount% = (50/800) × 100 = 6.25%
  • Final: Required discount is 6.25%, so option B is correct.

Q15): An item is sold at 10% loss. If selling price is increased by ₹33, it becomes 1% profit. Find CP.
A) ₹250
B) ₹275
C) ₹300
D) ₹330

Answer: C) ₹300

Explanation (Line-by-Line):

  • Step 1: Let CP = x, then SP₁ (10% loss) = 0.90x
  • Step 2: New SP₂ = 0.90x + 33 and 1% profit ⇒ SP₂ = 1.01x
  • Step 3: 0.90x + 33 = 1.01x ⇒ 33 = 0.11x ⇒ x = 300
  • Step 4: CP = ₹300
  • Final: Cost price is ₹300, so option C is correct.

Q16): A trader buys 220 pens at ₹10 each. He sells pens at ₹12 each, but gives 10% pens free (1 free for every 10 sold). Find profit percent (approx).
A) 8%
B) 9.09%
C) 10%
D) 11%

Answer: B) 9.09%

Explanation (Line-by-Line):

  • Step 1: “1 free for every 10 sold” means total pens = 11 parts, sold pens = 10 parts
  • Step 2: Out of 220 pens, sold pens = (10/11)×220 = 200
  • Step 3: Revenue = 200 × 12 = 2400 and total cost = 220 × 10 = 2200
  • Step 4: Profit% = (2400 − 2200)/2200 × 100 = 9.09%
  • Final: Profit percent is about 9.09%, so option B is correct.

Q17): A trader marks an item 40% above CP. At what discount percent will he incur a 5% loss?
A) 30%
B) 32.14%
C) 35%
D) 37.5%

Answer: B) 32.14%

Explanation (Line-by-Line):

  • Step 1: MP = 1.40 × CP and required SP for 5% loss = 0.95 × CP
  • Step 2: SP = MP × (1 − d) ⇒ 0.95CP = 1.40CP(1 − d)
  • Step 3: (1 − d) = 0.95/1.40 = 0.67857
  • Step 4: d = 1 − 0.67857 = 0.32143 = 32.14%
  • Final: Required discount is 32.14%, so option B is correct.

Q18): Two items are sold at the same selling price. On the first item profit is 25% and on the second item loss is 20%. Find the ratio of their cost prices (CP₁ : CP₂).
A) 4 : 5
B) 5 : 4
C) 16 : 25
D) 25 : 16

Answer: C) 16 : 25

Explanation (Line-by-Line):

  • Step 1: Let common SP = S
  • Step 2: CP₁ = S/1.25 and CP₂ = S/0.80
  • Step 3: CP₁ : CP₂ = (S/1.25) : (S/0.80) = 0.80 : 1.25
  • Step 4: 0.80 : 1.25 = 80 : 125 = 16 : 25
  • Final: Ratio is 16 : 25, so option C is correct.

Q19): A trader sells an item at 30% profit. If he sells it for ₹130 less, profit becomes 10%. Find the original selling price.
A) ₹820
B) ₹845
C) ₹870
D) ₹900

Answer: B) ₹845

Explanation (Line-by-Line):

  • Step 1: Let CP = x, then SP₁ = 1.30x and SP₂ = 1.10x
  • Step 2: Given SP₁ − SP₂ = 130 ⇒ (1.30x − 1.10x) = 0.20x = 130
  • Step 3: x = 130/0.20 = 650
  • Step 4: Original SP = 1.30 × 650 = 845
  • Final: Original selling price is ₹845, so option B is correct.

Q20): A shopkeeper buys an item for ₹1200, marks it 30% above CP, gives 10% discount, and pays commission 5% on SP. Find net profit percent (approx).
A) 9.5%
B) 10%
C) 11.15%
D) 12.5%

Answer: C) 11.15%

Explanation (Line-by-Line):

  • Step 1: MP = 1200 × 1.30 = 1560, so SP = 1560 × 0.90 = 1404
  • Step 2: Commission = 5% of 1404 = 70.2, net receipt = 1404 − 70.2 = 1333.8
  • Step 3: Profit = 1333.8 − 1200 = 133.8
  • Step 4: Profit% = (133.8/1200) × 100 = 11.15%
  • Final: Net profit percent is about 11.15%, so option C is correct.

This Tutorial is Related to: Aptitude Mcqs, Commission, Cp Sp, Discount, False Weight, Hard Level, Marked Price, Overall Profit Loss, Profit &Amp; Loss, Profit &Amp; Loss Questions, Pyq Pattern, Successive Discount, Ugc Net Paper 1, Unit 5

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