Profit and Loss
- A fruit vendor bought bananas at the rate of 5 for a rupee and sold them 4 for a rupee. The per cent gain or loss is
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Let the vendor buy 20 (LCM of 5 and 4) bananas.
CP of 5 bananas = $ 1
∴ CP of 20 bananas = $ 4
and SP of 4 bananas = $ 1
∴ SP of 20 bananas = $ 5
Gain = SP of 20 bananas - CP of 20 bananas = 5 - 4 = $ 1∴ Gain % = 1 × 100 = 25% 4
Second method to solve this question :
Here, a = 5, p = 1 and b = 4, q = 1Gain % = 
aq - bp 
× 100% bp
Correct Option: C
Let the vendor buy 20 (LCM of 5 and 4) bananas.
CP of 5 bananas = $ 1
∴ CP of 20 bananas = $ 4
and SP of 4 bananas = $ 1
∴ SP of 20 bananas = $ 5
Gain = SP of 20 bananas - CP of 20 bananas = 5 - 4 = $ 1∴ Gain % = 1 × 100 = 25% 4
Second method to solve this question :
Here, a = 5, p = 1 and b = 4, q = 1Gain % = aq - bp × 100% bp Gain % = 5 × 1 - 4 × 1 × 100% 4 × 1 Gain % = 1 × 100% = 25% 4
- A man sold 20 apples for $ 100 and gained 20%. How many apples did he buy for $ 100?
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If the CP of 20 apples be y, then
y × 120 = 100 100 ⇒ y = 100 × 100 = $ 250 120 3 ∵ $ 250 = 20 apples 3 ∴ $ 100 = 20 × 3 × 100 = 24 apples 250
We can find required answer with the help of given formula :
Here, a = ?, p = 100 and b = 20, q = 100
Gain% = 20%Gain % = aq - bp × 100% bp
Correct Option: C
If the CP of 20 apples be y, then
y × 120 = 100 100 ⇒ y = 100 × 100 = $ 250 120 3 ∵ $ 250 = 20 apples 3 ∴ $ 100 = 20 × 3 × 100 = 24 apples 250
We can find required answer with the help of given formula :
Here, a = ?, p = 100 and b = 20, q = 100
Gain% = 20%Gain % = aq - bp × 100% bp 20 % = a × 100 - 20 × 100 × 100% 20 × 100
⇒ 400 = 100a – 2000
⇒ 2400 = 100a ⇒ a = 24
- A man purchased some eggs at 3 for $ 5 and sold them at 5 for $ 12. Thus he gained $ 143 in all. The number of eggs he bought is
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Let he buy 15 eggs. [∴ LCM of 5 & 3 = 15 ]
CP of 3 eggs = $ 5
∴ CP of 15 eggs = $ 25
SP of 5 eggs = $ 12
∴ SP of 15 eggs = $ 36
∴ Gain = SP of 15 eggs - CP of 15 eggs = 36 – 25 = $ 11Correct Option: C
Let he buy 15 eggs. [∴ LCM of 5 & 3 = 15 ]
CP of 3 eggs = $ 5
∴ CP of 15 eggs = $ 25
SP of 5 eggs = $ 12
∴ SP of 15 eggs = $ 36
∴ Gain = SP of 15 eggs - CP of 15 eggs = 36 – 25 = $ 11
∵ $ 11 = 15 eggs∴ $ 143 = 15 × 143 = 195 eggs 11
- A man bought oranges at the rate of 8 for $ 34 and sold them at the rate of 12 for $ 57. How many oranges should be sold to earn a net profit of $ 45?
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Let the man buys 24 oranges. ( ∴ LCM of 8 and 12 = 24 )
C.P. of 8 oranges = $ 34∴ C.P. of 24 oranges = 34 × 24 = $ 102 8
S.P. of 12 oranges = $ 57∴ S.P. of 24 oranges = 57 × 24 = $ 114 12
Correct Option: A
Let the man buys 24 oranges. ( ∴ LCM of 8 and 12 = 24 )
C.P. of 8 oranges = $ 34∴ C.P. of 24 oranges = 34 × 24 = $ 102 8
S.P. of 12 oranges = $ 57∴ S.P. of 24 oranges = 57 × 24 = $ 114 12
Gain = S.P. of 24 oranges - C.P. of 24 oranges = 114 – 102 = $ 12
∵ 12 = 24 oranges∴ $ 45 = 24 × 45 = 90 oranges 12
- If toys are bought at $ 5 each and sold at $ 4.50 each, then the loss percent is :
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Loss = CP - SP = 5 – 4.50 = 0.50
∴ Loss percent = 0.50 × 100 = 10% 5
We can find required answer with the help of given formula :
Here, a = b, p = 5a and y = 4.50aLoss % = aq - bp × 100% bp
Correct Option: A
Loss = CP - SP = 5 – 4.50 = 0.50
∴ Loss percent = 0.50 × 100 = 10% 5
We can find required answer with the help of given formula :
Here, a = b, p = 5a and y = 4.50aLoss % = aq - bp × 100% bp Loss % = 4.50a2 - 5a2 × 100% 5a2 Loss % = - 0.5a2 × 100% 5a2
Loss % = 10% (–ve sign shows loss)
