Exercise: 8-A
Q1: Multiple Choice Type
i. 10 articles are bought for ₹40 and are sold at ₹5 per article. The profit / loss made is:
Step 1: C.P. of 10 articles = ₹40 ⇒ C.P. of 1 article = 40 ÷ 10 = ₹4
Step 2: S.P. of 1 article = ₹5
Step 3: Profit = S.P. – C.P. = 5 – 4 = ₹1
Step 4: Profit % = (Profit ÷ C.P.) × 100 = (1 ÷ 4) × 100 = 25%
Answer: b. 25% profit
ii. A table is sold at 80% of its cost price. The profit or loss as percent is:
Step 1: Let C.P. be ₹100
Step 2: S.P. = 80% of ₹100 = ₹80
Step 3: Loss = C.P. – S.P. = 100 – 80 = ₹20
Step 4: Loss % = (Loss ÷ C.P.) × 100 = (20 ÷ 100) × 100 = 20%
Answer: a. 20% loss
iii. C.P. = ₹150 and loss = ₹50, the S.P. is:
Step 1: S.P. = C.P. – Loss = 150 – 50 = ₹100
Answer: b. ₹100
iv. C.P. = ₹150 and loss = 50%, the S.P. is:
Step 1: Loss = 50% of ₹150 = (50 ÷ 100) × 150 = ₹75
Step 2: S.P. = C.P. – Loss = 150 – 75 = ₹75
Answer: d. ₹75
v. S.P. = ₹250 and profit = 25%, the C.P. is:
Step 1: Let C.P. = x
Step 2: Profit = 25% of x = (25 ÷ 100) × x = 0.25x
Step 3: S.P. = C.P. + Profit = x + 0.25x = 1.25x
Step 4: 1.25x = ₹250 ⇒ x = 250 ÷ 1.25 = ₹200
Answer: c. ₹200
vi. C.P. = ₹400 and overheads = ₹100. If loss = 10%; the S.P. is:
Step 1: Total cost = C.P. + Overheads = 400 + 100 = ₹500
Step 2: Loss = 10% of ₹500 = (10 ÷ 100) × 500 = ₹50
Step 3: S.P. = Total Cost – Loss = 500 – 50 = ₹450
Answer: c. ₹450
Q2: A fruit-seller buys oranges at 4 for ₹8 and sells them at 3 for ₹9. Find his profit percent.
Step 1: C.P. of 4 oranges = ₹8 ⇒ C.P. of 1 orange = 8 ÷ 4 = ₹2
Step 2: S.P. of 3 oranges = ₹9 ⇒ S.P. of 1 orange = 9 ÷ 3 = ₹3
Step 3: Profit per orange = S.P. – C.P. = 3 – 2 = ₹1
Step 4: Profit % = (Profit ÷ C.P.) × 100 = (1 ÷ 2) × 100 = 50%
Answer: Profit = 50%
Q3: A man buys a certain number of articles at 15 for ₹112.50 and sells them at 12 for ₹108. Find:
i. His gain as percent
Step 1: C.P. of 15 articles = ₹112.50
Step 2: C.P. of 1 article = ₹112.50 ÷ 15 = ₹7.50
Step 3: S.P. of 12 articles = ₹108 ⇒ S.P. of 1 article = ₹108 ÷ 12 = ₹9
Step 4: Profit per article = S.P. – C.P. = ₹9 – ₹7.50 = ₹1.50
Step 5: Profit % = (Profit ÷ C.P.) × 100 = (1.5 ÷ 7.5) × 100 = 20%
Answer: Gain = 20%
ii. The number of articles sold to make a profit of ₹75
Step 1: Profit per article = ₹1.50 (from part i)
Step 2: Total Profit required = ₹75
Step 3: Number of articles = Total Profit ÷ Profit per article = ₹75 ÷ ₹1.50 = 50 articles
Answer: 50 articles must be sold to earn ₹75 profit
Q4: A boy buys an old bicycle for ₹162 and spends ₹18 on its repairs before selling the bicycle for ₹207. Find his gain or loss percent.
Step 1: Cost Price (C.P.) of the bicycle = ₹162
Step 2: Repair cost = ₹18
Step 3: Total Cost Price = ₹162 + ₹18 = ₹180
Step 4: Selling Price (S.P.) = ₹207
Step 5: Profit = S.P. – C.P. = ₹207 – ₹180 = ₹27
Step 6: Profit % = (Profit ÷ C.P.) × 100 = (27 ÷ 180) × 100 = 15%
Answer: Gain = 15%
Q5: An article is bought from Jaipur for ₹4,800 and is sold in Delhi for ₹5,820. If ₹1,200 is spent on its transportations, etc., find the loss or the gain as percent.
Step 1: Purchase Price from Jaipur = ₹4,800
Step 2: Transportation and other expenses = ₹1,200
Step 3: Total Cost Price (C.P.) = ₹4,800 + ₹1,200 = ₹6,000
Step 4: Selling Price (S.P.) = ₹5,820
Step 5: Since S.P. < C.P., this is a loss
Step 6: Loss = C.P. – S.P. = ₹6,000 – ₹5,820 = ₹180
Step 7: Loss % = (Loss ÷ C.P.) × 100 = (180 ÷ 6000) × 100 = 3%
Answer: Loss = 3%
Q6: Mohit sold a T.V. for ₹3,600, gaining one-sixth of its selling price. Find:
i. The gain
Step 1: Selling Price (S.P.) = ₹3,600
Step 2: Gain = (1/6) of S.P. = (1/6) × 3600 = ₹600
Answer: Gain = ₹600
ii. The cost price of the T.V.
Step 1: C.P. = S.P. – Gain = ₹3,600 – ₹600 = ₹3,000
Answer: Cost Price = ₹3,000
iii. The gain percent
Step 1: Gain = ₹600, C.P. = ₹3,000
Step 2: Gain % = (Gain ÷ C.P.) × 100 = (600 ÷ 3000) × 100 = 20%
Answer: Gain Percent = 20%
Q7: By selling a certain number of goods for ₹5,500, a shopkeeper loses equal to one-tenth of their selling price. Find:
i. The loss incurred
Step 1: Selling Price (S.P.) = ₹5,500
Step 2: Loss = \(\frac{1}{10}\) of S.P. = \(\frac{1}{10}\) × ₹5,500 = ₹550
Answer: Loss = ₹550
ii. The cost price of the goods
Step 1: Cost Price (C.P.) = S.P. + Loss = ₹5,500 + ₹550 = ₹6,050
Answer: Cost Price = ₹6,050
iii. The loss as percent
Step 1: Loss = ₹550, C.P. = ₹6,050
Step 2: Loss % = \(\frac{550}{6050} \times 100\)
Step 3: Loss % ≈ \(\frac{11}{121} \times 100 = \frac{100}{11} = 9 \frac{1}{11}\%\)
Answer: Loss Percent = \(9 \frac{1}{11}\)%
Q8: The selling price of a sofa set is \(\frac{4}{5}\) times of its cost price. Find the gain or the loss as percent.
Step 1: Let the cost price (C.P.) of the sofa set be ₹100
Step 2: Then, selling price (S.P.) = \(\frac{4}{5} \times 100 = ₹80\)
Step 3: Since S.P. < C.P., there is a loss
Step 4: Loss = ₹100 – ₹80 = ₹20
Step 5: Loss % = \(\frac{20}{100} \times 100 = 20\%\)
Answer: Loss = 20%
Q9: The cost price of an article is \(\frac{4}{5}\) times of its selling price. Find the loss or the gain as percent.
Step 1: Let the selling price (S.P.) be ₹100
Step 2: Cost price (C.P.) = \(\frac{4}{5} \times 100 = ₹80\)
Step 3: Since C.P. < S.P., there is a gain
Step 4: Gain = ₹100 – ₹80 = ₹20
Step 5: Gain % = \(\frac{20}{80} \times 100 = 25\%\)
Answer: Gain = 25%
Q10: The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Step 1: Let the selling price (S.P.) be ₹100
Step 2: Cost price (C.P.) = 90% of ₹100 = ₹90
Step 3: Since C.P. < S.P., this is a profit
Step 4: Gain = ₹100 – ₹90 = ₹10
Step 5: Gain % = \(\frac{10}{90} \times 100 = \frac{1000}{90} = 11 \frac{1}{9}\%\)
Answer: Gain = \(11 \frac{1}{9}\)%
Q11: The cost price of an article is 30 percent less than its selling price. Find the profit or the loss as percent.
Step 1: Let the selling price (S.P.) be ₹100
Step 2: Cost price (C.P.) is 30% less than S.P.
Step 3: C.P. = ₹100 – 30% of ₹100 = ₹100 – ₹30 = ₹70
Step 4: Profit = S.P. – C.P. = ₹100 – ₹70 = ₹30
Step 5: Profit % = \(\frac{30}{70} \times 100 = \frac{3000}{70} = \frac{300}{7} = 42 \frac{6}{7}\%\)
Answer: Gain = \(42 \frac{6}{7}\)%
Q12: A shopkeeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transit and then he sold the remaining eggs at one rupee each. Find his gain or loss as percent.
Step 1: Cost Price of 1 egg = ₹0.80
Step 2: Total Cost Price = 300 × ₹0.80 = ₹240
Step 3: Number of eggs broken = 30
Step 4: Number of eggs sold = 300 – 30 = 270
Step 5: Selling Price per egg = ₹1
Step 6: Total Selling Price = 270 × ₹1 = ₹270
Step 7: Profit = S.P. – C.P. = ₹270 – ₹240 = ₹30
Step 8: Profit % = \(\frac{30}{240} \times 100 = 12.5\%\)
Answer: Gain = 12.5%
Q13: By selling an article for ₹900, a man gains 20%. Find his cost price and the gain.
Step 1: Let the Cost Price be ₹x
Step 2: Gain % = 20% ⇒ Selling Price = Cost Price + 20% of Cost Price
Step 3: S.P. = \(x + \frac{20}{100} \times x = \frac{120}{100} \times x = \frac{6}{5}x\)
Step 4: Given S.P. = ₹900 ⇒ \(\frac{6}{5}x = 900\)
Step 5: Multiply both sides by 5: \(6x = 4500\)
Step 6: Divide by 6: \(x = \frac{4500}{6} = 750\)
Step 7: Cost Price = ₹750
Step 8: Gain = S.P. – C.P. = ₹900 – ₹750 = ₹150
Answer: Cost Price = ₹750, Gain = ₹150
Q14: By selling an article for ₹704, a person loses 12%. Find his cost price and the loss.
Step 1: Let the Cost Price be ₹x
Step 2: Loss % = 12% ⇒ Selling Price = Cost Price − 12% of Cost Price
Step 3: S.P. = \(x – \frac{12}{100} \times x = \frac{88}{100} \times x = \frac{22}{25}x\)
Step 4: Given S.P. = ₹704 ⇒ \(\frac{22}{25}x = 704\)
Step 5: Multiply both sides by 25: \(22x = 17600\)
Step 6: Divide by 22: \(x = \frac{17600}{22} = 800\)
Step 7: Cost Price = ₹800
Step 8: Loss = C.P. − S.P. = ₹800 − ₹704 = ₹96
Answer: Cost Price = ₹800, Loss = ₹96
Q15: Find the selling price:
i. C.P. = ₹352, overheads = ₹28 and profit = 20%
Step 1: Total Cost Price = C.P. + Overheads = ₹352 + ₹28 = ₹380
Step 2: Profit = 20% of ₹380 = \(\frac{20}{100} \times 380 = ₹76\)
Step 3: Selling Price = C.P. + Profit = ₹380 + ₹76 = ₹456
Answer: S.P. = ₹456
ii. C.P. = ₹576, overheads = ₹44 and loss = 16%
Step 1: Total Cost Price = ₹576 + ₹44 = ₹620
Step 2: Loss = 16% of ₹620 = \(\frac{16}{100} \times 620 = ₹99.20\)
Step 3: Selling Price = C.P. − Loss = ₹620 − ₹99.20 = ₹520.80
Answer: S.P. = ₹520.80
Q16: If John sells his bicycle for ₹637, he will suffer a loss of 9%. For how much should it be sold if he desires a profit of 5%?
Step 1: Let the cost price (C.P.) be ₹x
Step 2: Given: Loss = 9%, so Selling Price = \(\frac{91}{100}x\)
Step 3: Selling Price = ₹637 ⇒ \(\frac{91}{100}x = 637\)
Step 4: Multiply both sides by 100: \(91x = 63700\)
Step 5: Divide by 91: \(x = \frac{63700}{91} = ₹700\)
Step 6: So, Cost Price = ₹700
Step 7: To gain 5%, required Selling Price = \(\frac{105}{100} \times 700 = ₹735\)
Answer: To gain 5%, John should sell the bicycle for ₹735
Q17: A man sells a radio set for ₹605 and gains 10%. At what price should he sell another radio of the same kind in order to gain 16%?
Step 1: Let the cost price (C.P.) be ₹x
Step 2: Given: 10% gain on ₹x ⇒ Selling Price = \(\frac{110}{100}x = \frac{11}{10}x\)
Step 3: Selling Price = ₹605 ⇒ \(\frac{11}{10}x = 605\)
Step 4: Multiply both sides by 10: \(11x = 6050\)
Step 5: Divide by 11: \(x = \frac{6050}{11} = ₹550\)
Step 6: So, Cost Price = ₹550
Step 7: To gain 16%, required Selling Price = \(\frac{116}{100} \times 550 = ₹638\)
Answer: He should sell it for ₹638 to gain 16%
Q18: By selling a sofa set for ₹2,500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa set for ₹3,150.
Step 1: Let the Cost Price (C.P.) be ₹x
Step 2: Given: 20% loss ⇒ Selling Price = \(\frac{80}{100}x = \frac{4}{5}x\)
Step 3: \(\frac{4}{5}x = 2500\)
Step 4: Multiply both sides by 5: \(4x = 12,500\)
Step 5: Divide by 4: \(x = \frac{12500}{4} = ₹3,125\)
Step 6: So, Cost Price = ₹3,125
Step 7: New Selling Price = ₹3,150
Step 8: Profit = S.P. − C.P. = ₹3,150 − ₹3,125 = ₹25
Step 9: Profit % = \(\frac{25}{3125} \times 100 = 0.8\%\)
Answer: Profit Percent = 0.8%
