Exercise: 7-E
Multiple Choice Questions
Q1: By selling an article for ₹100, one gains ₹10. The gain per cent is
Step 1: Let the Selling Price (S.P.) = ₹100
Gain = ₹10
Step 2: Use formula:
\[
\text{Gain} = \text{S.P.} – \text{C.P.} \\
\Rightarrow \text{C.P.} = \text{S.P.} – \text{Gain} = 100 – 10 = ₹90
\]Step 3: Gain% is given by:
\[
\text{Gain%} = \left( \frac{\text{Gain}}{\text{C.P.}} \right) \times 100 = \left( \frac{10}{90} \right) \times 100 = \frac{1000}{90} = 11\frac{1}{9}%
\]Answer: d. \(11\frac{1}{9}\)%
Q2: By selling an article for ₹100, one loses ₹10. The loss per cent is
Step 1: Given:
Selling Price (S.P.) = ₹100
Loss = ₹10
Step 2: Use the formula:
\[
\text{Loss} = \text{C.P.} – \text{S.P.} \\
\Rightarrow \text{C.P.} = \text{S.P.} + \text{Loss} = 100 + 10 = ₹110
\]Step 3: Loss% is given by:
\[
\text{Loss%} = \left( \frac{\text{Loss}}{\text{C.P.}} \right) \times 100 = \left( \frac{10}{110} \right) \times 100 = \frac{1000}{110} = 9\frac{1}{11}%
\]Answer: b. \(9\frac{1}{11}\)%
Q3: A man sold his cow for ₹7920 and gained 10%. The cow was bought for
Step 1: Let the Cost Price (C.P.) be ₹x.
Given: Gain = 10%, Selling Price (S.P.) = ₹7920
Step 2: Use the formula:
\[
\text{S.P.} = \left(1 + \frac{\text{Gain%}}{100}\right) \times \text{C.P.} \\
\Rightarrow 7920 = \left(1 + \frac{10}{100}\right) \times x = \frac{110}{100} \times x
\]Step 3: Solve for x:
\[
x = \frac{7920 \times 100}{110} = \frac{792000}{110} = ₹7200
\]Answer: b. ₹7200
Q4: A watch is sold for ₹1080 at a loss of 10%. The cost price of the watch is
Step 1: Let the Cost Price (C.P.) be ₹x.
Loss = 10%, and Selling Price (S.P.) = ₹1080
Step 2: Use the formula:
\[
\text{S.P.} = \left(1 – \frac{\text{Loss%}}{100}\right) \times \text{C.P.} \\
\Rightarrow 1080 = \left(1 – \frac{10}{100}\right) \times x = \frac{90}{100} \times x
\]Step 3: Solve for x:
\[
x = \frac{1080 \times 100}{90} = \frac{108000}{90} = ₹1200
\]Answer: b. ₹1200
Q5: By selling an article for ₹240, a trader loses 4%. In order to gain 10%, he must sell that article for
Step 1: Let the Cost Price (C.P.) be ₹x.
Loss = 4%, and S.P. = ₹240
Use formula for loss:
\[
\text{S.P.} = \left(1 – \frac{\text{Loss%}}{100} \right) \times \text{C.P.} \\
\Rightarrow 240 = \frac{96}{100} \times x \\
\Rightarrow x = \frac{240 \times 100}{96} = ₹250
\]Step 2: To gain 10%, Selling Price should be:
\[
\text{S.P.} = \left(1 + \frac{10}{100}\right) \times 250 = \frac{110}{100} \times 250 = ₹275
\]Answer: c. ₹275
Q6: A man loses ₹20 by selling some articles at the rate of ₹3 per piece and gains ₹30, if he sells them at ₹3.25 per piece. The number of pieces sold by him is
Step 1: Let the number of pieces sold be \( x \).
Selling Price at ₹3 per piece = \( 3x \)
Selling Price at ₹3.25 per piece = \( 3.25x \)
Loss at ₹3 per piece = ₹20
Gain at ₹3.25 per piece = ₹30
Step 2: Use the relation:
\[
\text{Profit} – \text{Loss} = (3.25x – C.P.) – (C.P. – 3x) = ₹30 – (-₹20) = ₹50
\]
Or simply,
\[
\text{Difference in S.P.} = ₹50 \\
\Rightarrow 3.25x – 3x = 0.25x = 50 \\
\Rightarrow x = \frac{50}{0.25} = 200
\]Answer: c. 200
Q7: The per cent profit made when an article is sold for ₹78 is twice as when it is sold for ₹69. The cost price of the article is
Step 1: Let the cost price be ₹x.
Profit when sold at ₹78 = \(78 – x\)
Profit when sold at ₹69 = \(69 – x\)
Given:
\[
\frac{78 – x}{x} = 2 \times \frac{69 – x}{x}
\]Or equivalently:
\[
\text{Profit% at ₹78} = 2 \times \text{Profit% at ₹69}
\]Step 2: Multiply both sides by \( x \):
\[
78 – x = 2(69 – x)
\]Step 3: Expand and simplify:
\[
78 – x = 138 – 2x \\
\Rightarrow 78 + x = 138 \\
\Rightarrow x = 138 – 78 = ₹60
\]Answer: d. ₹60
Q8: A vendor buys oranges at ₹2 for 3 oranges and sells them at a rupee each. To make a profit of ₹10 he must sell
Step 1: Cost Price (C.P.) of 3 oranges = ₹2
So, C.P. of 1 orange = ₹\(\frac{2}{3}\)
Selling Price (S.P.) of 1 orange = ₹1
Step 2: Profit per orange = S.P. – C.P.
\[
= 1 – \frac{2}{3} = \frac{1}{3} \text{ ₹ per orange}
\]Step 3: Let the number of oranges sold be \( x \)
Total profit = ₹10
\[
\frac{1}{3}x = 10 \Rightarrow x = 10 \times 3 = 30
\]Answer: c. 30 oranges
Q9: A man gains 10% by selling an article for a certain price. If he sells it at double the price the profit made is
Step 1: Let the Cost Price (C.P.) be ₹100.
Given: Profit = 10%, so Selling Price (S.P.) = ₹110
Step 2: Now, new S.P. = double of ₹110 = ₹220
Step 3: New Profit = S.P. – C.P.
\[
\text{Profit} = 220 – 100 = ₹120
\]Step 4: Profit% = \(\frac{Profit}{C.P.} \times 100 = \frac{120}{100} \times 100 = 120\%\)
Answer: d. 120%
Q10: If an article is sold at a gain of 6% instead of at a loss of 6%, then the seller gets ₹6 more. The cost price of the article is
Step 1: Let the cost price be ₹x.
S.P. at 6% gain = \( x + 6\% \text{ of } x = x + \frac{6}{100}x = \frac{106}{100}x \)
S.P. at 6% loss = \( x – 6\% \text{ of } x = x – \frac{6}{100}x = \frac{94}{100}x \)
Step 2: Difference between the two selling prices is ₹6
\[
\frac{106}{100}x – \frac{94}{100}x = \frac{12}{100}x = 6 \\
\Rightarrow x = \frac{6 \times 100}{12} = ₹50
\]Answer: a. ₹50
Q11: A radio is sold at a gain of 16%. If it had been sold for ₹20 more, 20% would have been gained, The cost price of the radio is
Step 1: Let the Cost Price (C.P.) be ₹x.
Then Selling Price at 16% gain = \( \frac{116}{100}x \)
Selling Price at 20% gain = \( \frac{120}{100}x \)
Step 2: Difference in S.P. = ₹20
\[
\frac{120}{100}x – \frac{116}{100}x = \frac{4}{100}x = 20 \\
\Rightarrow x = \frac{20 \times 100}{4} = ₹500
\]Answer: c. ₹500
Q12: Profit after selling an article for ₹425 is the same as loss after selling it for ₹355. The cost of the article is
Step 1: Let the Cost Price (C.P.) be ₹x.
If article is sold for ₹425 → profit = \(425 – x\)
If article is sold for ₹355 → loss = \(x – 355\)
Given: Profit = Loss
\[
425 – x = x – 355
\]Step 2: Solve the equation:
\[
425 + 355 = 2x \Rightarrow 780 = 2x \Rightarrow x = \frac{780}{2} = ₹390
\]Answer: b. ₹390
Q13: A sold a watch to B at a gain of 5% and B sold it to C at again of 4%. If C paid ₹1092 for it the price paid by A is
Step 1: Let the price paid by A be ₹x.
A sells to B at 5% gain → B’s price = \(x + 5\%\text{ of }x = x \times \frac{105}{100} = \frac{105}{100}x\)
B sells to C at 4% gain → C’s price = \(\frac{105}{100}x \times \frac{104}{100} = \frac{10920}{10000}x\)
Step 2: Given: C paid ₹1092
\[
\frac{10920}{10000}x = 1092 \\
\Rightarrow x = \frac{1092 \times 10000}{10920} = \frac{10920000}{10920} \\
\Rightarrow x = ₹1000
\]Answer: d. ₹1000
Q14: A bicycle is sold at a gain of 16%. If it had been sold for ₹60 more, 20% would have been gained. The cost price of the bicycle is
Step 1: Let the cost price of the bicycle be ₹x.
Selling Price at 16% gain = \(\frac{116}{100}x\)
Selling Price at 20% gain = \(\frac{120}{100}x\)
Step 2: Given difference in selling price = ₹60
\[
\frac{120}{100}x – \frac{116}{100}x = \frac{4}{100}x = 60 \\
\Rightarrow x = \frac{60 \times 100}{4} = ₹1500
\]Answer: c. ₹1500
Q15: If the cost price of 15 tables be equal to selling price of 20 tables, the loss per cent is
Step 1: Let the Cost Price of 1 table be ₹1.
Then, C.P. of 15 tables = ₹15
S.P. of 20 tables = ₹15 ⇒ S.P. of 1 table = ₹\(\frac{15}{20} = 0.75\)
Step 2: Loss on 1 table = C.P. – S.P. = ₹1 – ₹0.75 = ₹0.25
Step 3: Loss % = \(\frac{0.25}{1} \times 100 = 25\%\)
Answer: b. 25%
Q16: A fruit seller buys lemons at 2 for a rupee and sells them at 5 for ₹3. His gain per cent is
Step 1: Cost Price (C.P.) of 2 lemons = ₹1
So, C.P. of 1 lemon = ₹\(\frac{1}{2}\)
Step 2: Selling Price (S.P.) of 5 lemons = ₹3
So, S.P. of 1 lemon = ₹\(\frac{3}{5}\)
Step 3: Gain per lemon = S.P. – C.P.
\[
= \frac{3}{5} – \frac{1}{2} = \frac{6 – 5}{10} = \frac{1}{10}
\]Step 4: Gain % = \(\frac{1}{10} \div \frac{1}{2} \times 100 = \frac{1}{10} \times \frac{2}{1} \times 100 = 20\%\)
Answer: c. 20%
Q17: By gelling 45 oranges for ₹80 a man loses 20%, How many should he sell for ₹48 so as to gain in the transaction?
Step 1: First, find the Cost Price (C.P.) of 45 oranges.
Loss = 20% ⇒ S.P. = 80% of C.P.
\[
\text{S.P. of 45 oranges} = ₹80 = \frac{80}{100} \times \text{C.P.} \\
\Rightarrow \text{C.P.} = \frac{80 \times 100}{80} = ₹100
\]Step 2: C.P. of 45 oranges = ₹100 ⇒ C.P. of 1 orange = ₹\(\frac{100}{45}\)
Step 3: Let him sell \(x\) oranges for ₹48 to make neither loss nor gain (i.e., S.P. = C.P.)
C.P. of \(x\) oranges = \(x \times \frac{100}{45}\)
Set it equal to ₹48:
\[
x \times \frac{100}{45} = 48 \Rightarrow x = \frac{48 \times 45}{100} = 21.6
\]So, to gain in the transaction, he must sell fewer than 21.6 oranges for ₹48.
Now check the options:
a. 15 ⇒ too few (profit too high?)
b. 18 ⇒ try it:
\[
\text{C.P. of 18 oranges} = \frac{100}{45} \times 18 = ₹40 \\
\Rightarrow \text{Profit} = ₹48 – ₹40 = ₹8 \\
\Rightarrow \text{Profit %} = \frac{8}{40} \times 100 = 20\% ✅
\]Answer: b. 18
Q18: A trader lists his articles 20% above cost price and allows a discount of 10% on cash payment. His gain percent is
Step 1: Let the Cost Price (C.P.) be ₹100.
Marked Price (M.P.) = ₹100 + 20% of ₹100 = ₹120
Discount = 10% of ₹120 = ₹12
Selling Price (S.P.) = ₹120 − ₹12 = ₹108
Step 2: Profit = S.P. − C.P. = ₹108 − ₹100 = ₹8
Profit % = \(\frac{8}{100} \times 100 = 8\%\)
Answer: c. 8%
Q19: At what percent above the cost price must an article be marked so as to gain 22.5% after allowing a discount of 2%?
Step 1: Let the Cost Price (C.P.) = ₹100
Gain = 22.5% ⇒ Selling Price (S.P.) = ₹122.50
Step 2: Let the Marked Price (M.P.) be ₹x.
Discount = 2% ⇒ S.P. = 98% of M.P. = \(\frac{98}{100} \times x\)
So,
\[
\frac{98}{100}x = 122.5 \Rightarrow x = \frac{122.5 \times 100}{98} = 125
\]Step 3: Marked price = ₹125
Cost price = ₹100
Required % above cost price = \(\frac{125 – 100}{100} \times 100 = 25\%\)
Answer: c. 25%
Q20: Arun buys an article with 25% discount on its marked price. He makes a profit of 10% by selling it at ₹660. The marked price is
Step 1: Let the marked price be ₹x.
Discount = 25% ⇒ Cost Price (C.P.) = 75% of x = \(\frac{75}{100}x = \frac{3}{4}x\)
Step 2: Arun earns 10% profit on C.P.
Selling Price (S.P.) = ₹660
\[
660 = \text{C.P.} + 10\% \text{ of C.P.} = \frac{110}{100} \times \frac{3}{4}x = \frac{33}{40}x
\]Step 3: Solve for x:
\[
\frac{33}{40}x = 660 \Rightarrow x = \frac{660 \times 40}{33} = ₹800
\]Answer: c. ₹800
Q21: An umbrella marked at ₹80 is sold for ₹68. The rate of discount is
Step 1: Marked Price (M.P.) = ₹80
Selling Price (S.P.) = ₹68
Discount = ₹80 − ₹68 = ₹12
Step 2: Rate of Discount = \(\frac{\text{Discount}}{\text{Marked Price}} \times 100\)
\[
= \frac{12}{80} \times 100 = 15\%
\]Answer: b. 15%
Q22: A tradesman marks his goods 30% above cost price. If he allows a discount of \(6\frac{1}{4}\)%, then his gain per cent is
Step 1: Let the Cost Price (C.P.) = ₹100
Marked Price (M.P.) = ₹100 + 30% of ₹100 = ₹130
Step 2: Discount = \(6\frac{1}{4}\%\) = \(\frac{25}{4}\)%
Discount amount = \(\frac{25}{4} \% \text{ of } ₹130 = \frac{25}{4} \times \frac{130}{100} = ₹8.125\)
Step 3: Selling Price (S.P.) = ₹130 − ₹8.125 = ₹121.875
Step 4: Gain = S.P. − C.P. = ₹121.875 − ₹100 = ₹21.875
Gain % = \(\frac{21.875}{100} \times 100 = 21.875\% = 21\frac{7}{8}\%\)
Answer: a. \(21\frac{7}{8}\)%
Q23: A discount series of 10%, 20% and 40% is equivalent to a single discount of
Step 1: Assume Marked Price (M.P.) = ₹100
Step 2: First discount = 10% of ₹100 = ₹10 ⇒ New Price = ₹90
Second discount = 20% of ₹90 = ₹18 ⇒ New Price = ₹72
Third discount = 40% of ₹72 = ₹28.80 ⇒ Final Price = ₹72 − ₹28.80 = ₹43.20
Step 3: Net Discount = ₹100 − ₹43.20 = ₹56.80
Single Discount % = \(\frac{56.80}{100} \times 100 = 56.8\%\)
Answer: b. 56.8%
Q24: The difference between a discount of 40% on ₹500 and two successive discounts of 36% and 4% on the same amount is
Step 1: Apply single discount of 40% on ₹500:
\[
\text{Single Discount Price} = ₹500 – 40\% \text{ of } ₹500 = ₹500 – ₹200 = ₹300
\]Step 2: Apply successive discounts of 36% and 4%:
First discount = 36% of ₹500 = ₹180 ⇒ New Price = ₹500 − ₹180 = ₹320
Second discount = 4% of ₹320 = ₹12.80 ⇒ Final Price = ₹320 − ₹12.80 = ₹307.20
Step 3: Difference in price = ₹307.20 − ₹300 = ₹7.20
Answer: d. ₹7.20
Q25: On an article with marked price ₹20000, a customer has a choice between three successive discounts of 20%, 20% and 10% and three successive discounts of 40%, 5% and 5%. By choosing the better offer he can save
Step 1: Calculate Net Price for Discount Series 1: 20%, 20%, 10%
Marked Price = ₹20000
First Discount = 20% of ₹20000 = ₹4000 ⇒ Price = ₹16000
Second Discount = 20% of ₹16000 = ₹3200 ⇒ Price = ₹12800
Third Discount = 10% of ₹12800 = ₹1280 ⇒ Final Price = ₹12800 − ₹1280 = ₹11520
Step 2: Calculate Net Price for Discount Series 2: 40%, 5%, 5%
First Discount = 40% of ₹20000 = ₹8000 ⇒ Price = ₹12000
Second Discount = 5% of ₹12000 = ₹600 ⇒ Price = ₹11400
Third Discount = 5% of ₹11400 = ₹570 ⇒ Final Price = ₹11400 − ₹570 = ₹10830
Step 3: Compare both options:
Discount Series 1 Final Price = ₹11520
Discount Series 2 Final Price = ₹10830
Saving = ₹11520 − ₹10830 = ₹690
Answer: b. ₹690
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