Profit and Loss
- A fruit-seller buys some oranges and by selling 40% of them he realises the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells 80% of the remaining oranges at half the previous rate of profit. The rest of the oranges being rotten are thrown away. The overall percentage of profit is
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Let Number of oranges bought = 100
And C.P. of oranges = $ 100
S.P of 40 oranges = $ 100
Gain on 40 Oranges = 100 - 40 = $ 60∴ Gain percent = 60 × 100 = 150 % 40
Remaining oranges = 60Their 80 % = 60 × 80 = 48 100
Correct Option: B
Let Number of oranges bought = 100
And C.P. of oranges = $ 100
S.P of 40 oranges = $ 100
Gain on 40 Oranges = 100 - 40 = $ 60∴ Gain percent = 60 × 100 = 150 % 40
Remaining oranges = 60Their 80 % = 60 × 80 = 48 100
These are sold at a profit of 75 % .∴ Their S.P. = 48 × 175 = $ 84 100
12 oranges was rotten so he threw away.
∴ Total SP = 100 + 84 = $ 184
Gain = Total SP - CP = 184 - 100 = $ 84∴ Gain percent = 84 × 100 = 84% 100
- A shop-keeper sold a sewing machine for $ 1,080 at a loss of 10%. At what price should he has to sold it so as to gain 10% on it ? (in $ )
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Here , Selling Price of sewing machine = $ 1080
at a loss of 10% ,Cost price of sewing machine = 1080 × 100 = $1200 90
Correct Option: D
Here , Selling Price of sewing machine = $ 1080
at a loss of 10% ,Cost price of sewing machine = 1080 × 100 = $1200 90 ∴ S.P. for a profit of 10% = 1200 × 110 = $1320 100
- If I purchased 11 books for $ 100 and sold 10 books for $ 110, the percentage of profit per book sold is
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If a articles are bought for $ p
and b articles are sold for $ q,
thenGain% = qa - pb × 100 pb Gain% = 11 × 110 - 10 × 100 × 100 10 × 100 Gain % = 1210 - 1000 × 100 = 21% 1000
Second method to solve this question :
Here, a = 11, p = 100 and b = 10, y = 110Gain% = aq - bp × 100% bp
Correct Option: D
If a articles are bought for $ p
and b articles are sold for $ q,
thenGain% = qa - pb × 100 pb Gain% = 11 × 110 - 10 × 100 × 100 10 × 100 Gain % = 1210 - 1000 × 100 = 21% 1000
Second method to solve this question :
Here, a = 11, p = 100 and b = 10, y = 110Gain% = aq - bp × 100% bp Gain% = 11 × 110 - 10 × 100 × 100 10 × 100 Gain% = 1210 - 1000 × 100% = 21% 1000
- A vendor sells lemons at the rate of 5 for $ 14, gaining thereby 40%. For how much did he buy a dozen lemons?
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Given that , S.P. of 5 lemons = $ 14
On gain 40% ,C.P. of 5 lemons = 100 × 14 = $ 10 140 ∴ C.P. of 12 lemons = 10 × 21 = $ 24 5
We can find required answer with the help of given formula :
Here, a = 12, p = ? and b = 5, q = 14, Gain% = 40%Gain% = aq - bp × 100% bp
Correct Option: C
Given that , S.P. of 5 lemons = $ 14
On gain 40% ,C.P. of 5 lemons = 100 × 14 = $ 10 140 ∴ C.P. of 12 lemons = 10 × 21 = $ 24 5
We can find required answer with the help of given formula :
Here, a = 12, p = ? and b = 5, q = 14, Gain% = 40%Gain% = aq - bp × 100% bp 40% = 12 × 14 - 5 × p × 100% 5p
⇒ 2p = 168 – 5p
⇒ 7p = 168
⇒ p = 24
- A person bought 50 pens for $ 50 each. He sold 40 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain per cent on the remaining pens should be
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Here , C.P. of 1 pen = $ 50
∴ C.P. of 50 pens = 50 × 50 = $ 2500
For profit of 10% ,S.P. = 2500 × 110 = $ 2750 100 S.P. of 40 pens at a loss of 5% = 40 × 50 × 95 = $ 1900 100
∴ S.P. of remaining 10 pens = 2750 – 1900 = $ 850
Correct Option: D
Here , C.P. of 1 pen = $ 50
∴ C.P. of 50 pens = 50 × 50 = $ 2500
For profit of 10% ,S.P. = 2500 × 110 = $ 2750 100 S.P. of 40 pens at a loss of 5% = 40 × 50 × 95 = $ 1900 100
∴ S.P. of remaining 10 pens = 2750 – 1900 = $ 850
Gain = S.P. of remaining 10 pens - C.P. of remaining 10 pens = 850 - 500 = $ 350∴ Gain % = 350 × 100 = 70 % 500