Profit and Loss
- If an article is sold for $ 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11 %?
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Here , Selling Price of article = $ 178
The article is sold at 11% loss.
∴ ( 100 - 11 )% of CP = $ 178
⇒ 89% of CP = $ 178⇒ CP = $ 178 × 100 = $ 200 89
To gain 11% ,
New S.P. = 111% of $ 200
Correct Option: C
Here , Selling Price of article = $ 178
The article is sold at 11% loss.
∴ ( 100 - 11 )% of CP = $ 178
⇒ 89% of CP = $ 178⇒ CP = $ 178 × 100 = $ 200 89
To gain 11% ,
New S.P. = 111% of $ 200New S.P. = $ 111 × 200 = $ 222 100
- A man sells an article at 10% loss. If he had sold it at $ 10 more, he would have gained 10%. The cost price of the article is
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Let the C.P be $ y.
First selling price = 90% of y = $ 9y 10 Second selling price = 
9y + 10 
10 ∴ 110% of y = 9y + 10 10 ⇒ 11y = 9y + 10 ⇒ 2y = 10 10 10 10 ⇒ y = 10 × 10 = 50 = $ 50 2
We can find required answer with the help of given formula :
Here, a = 10%, R= 10, b = 10%
Correct Option: A
Let the C.P be $ y.
First selling price = 90% of y = $ 9y 10 Second selling price = 9y + 10 10 ∴ 110% of y = 9y + 10 10 ⇒ 11y = 9y + 10 ⇒ 2y = 10 10 10 10 ⇒ y = 10 × 10 = 50 = $ 50 2
We can find required answer with the help of given formula :
Here, a = 10%, R= 10, b = 10%C.P. = R × 100 b + a C.P. = 10 × 100 = $ 50 10 + 10
- A bookseller sells a book at a profit of 10%. If he had bought it at 4% less and sold it for $ 6 more, he would have gained (75 / 4) %. The cost price of the book is
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Let the CP of the book be $ y
Initial SP = 110 × y = 1.1 y 100
New CP = 0.96 yNew SP = 100 + 75 % of 0.96y 4 New SP = 475 × 0.96y = 1.14 y 400
Therefore, 1.14 y –1.1y = 6
⇒ 0.04 y = 6
Correct Option: C
Let the CP of the book be $ y
Initial SP = 110 × y = 1.1 y 100
New CP = 0.96 yNew SP = 100 + 75 % of 0.96y 4 New SP = 475 × 0.96y = 1.14 y 400
Therefore, 1.14 y –1.1y = 6
⇒ 0.04 y = 6⇒ y = 6 = 600 = 150 0.04 4
∴ CP = $ 150
- A man sells his typewriter at 5% loss. If he sells it for $ 80 more, he will gain 5%. The cost price of the typewriter is
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Let the CP of the typewriter be $ y.
At 5% loss, SP = 95y 100 Now, 95y + 80 = 105y 100 100 ⇒ 105y - 95y = 80 100 100 ⇒ 105y - 95y = 80 100 ⇒ y = 8000 = $ 800 10
Second method to solve this question :
Here, a = 5%, R = 80, b = 5%
Correct Option: D
Let the CP of the typewriter be $ y.
At 5% loss, SP = 95y 100 Now, 95y + 80 = 105y 100 100 ⇒ 105y - 95y = 80 100 100 ⇒ 105y - 95y = 80 100 ⇒ y = 8000 = $ 800 10
Second method to solve this question :
Here, a = 5%, R = 80, b = 5%C.P. = R × 100 b + a C.P. = 80 × 100 = $ 800 5 + 5
- A businessman sells a commodity at 10% profit. If he had bought it at 10% less and sold it for $ 2 less, then he would have gained (50 / 5) %. The cost price of the commodity is
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Let the first CP of the commodity be $ 100.
∴ First SP = $ 110
Second CP = $ 90Gain% = 50 % 3 ∴ Second SP = 100 + 50 % of 90 3 Second SP = $ 90 × 350 = $ 105 300
Difference of first and second S.P. = $ (110 – 105) = $ 5
∵ If the difference is $ 5, the CP = $ 100.
Correct Option: C
Let the first CP of the commodity be $ 100.
∴ First SP = $ 110
Second CP = $ 90Gain% = 50 % 3 ∴ Second SP = 100 + 50 % of 90 3 Second SP = $ 90 × 350 = $ 105 300
Difference of first and second S.P. = $ (110 – 105) = $ 5
∵ If the difference is $ 5, the CP = $ 100.
∵ If the difference be $ 2, theC.P. = 100 × 2 = $ 40 5
