Profit and Loss
- A man sold an article at a loss of 20%. If he had sold it for $ 50 more, he would have gained 5%. The cost price of the article was
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Let the CP of the article be $ y
SP of the article at 20% loss = y × 80 = 4y 100 5
In second case,4y + 50 = 105y 5 100 ⇒ 4y + 50 = 21y 5 20 ⇒ 21y - 4y = 50 20 5 ⇒ 21y - 16y = 50 20 ⇒ 5y = 50 20
⇒ y = $ 200
We can find required answer with the help of given formula :
Here, a = 20%, R = $ 50, b = 5%C.P. = R × 100 b + a
Correct Option: D
Let the CP of the article be $ y
SP of the article at 20% loss = y × 80 = 4y 100 5
In second case,4y + 50 = 105y 5 100 ⇒ 4y + 50 = 21y 5 20 ⇒ 21y - 4y = 50 20 5 ⇒ 21y - 16y = 50 20 ⇒ 5y = 50 20
⇒ y = $ 200
We can find required answer with the help of given formula :
Here, a = 20%, R = $ 50, b = 5%C.P. = R × 100 b + a C.P. = 50 × 100 20 + 5 C.P. = 50 × 100 = $ 200 25
- When an article is sold at a gain of 20%, it yields $ 60 more than when it is sold at a loss of 20%. The cost price of the article is
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Let the CP of the article be $ y
∴ 120y - 80y = 60 100 100
⇒ 40y = 60 × 100⇒ y = 60 × 100 = $ 150 40
We can find required answer with the help of given formula :
Here, a = 20%, R = $ 60, b= 20%C.P. = R × 100 b + a
Correct Option: B
Let the CP of the article be $ y
∴ 120y - 80y = 60 100 100
⇒ 40y = 60 × 100⇒ y = 60 × 100 = $ 150 40
We can find required answer with the help of given formula :
Here, a = 20%, R = $ 60, b= 20%C.P. = R × 100 b + a C.P. = 60 × 100 20 + 20 C.P. = 6000 = $ 150 40
- Aniruddha sold a bicycle at a gain of 8%. Had it been sold for $ 75 more, the gain would have been 14%. The cost price of the bicycle was
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Let the CP of cycle be $ y
S.P. = 108y 100 108y + 75 = 114y 100 100
⇒ 108y + 7500 = 114y
⇒ 114y – 108y = 7500
⇒ 6y = 7500⇒ y = 7500 = $ 1250 6
We can find required answer with the help of given formula :
Here, a = 8%, R= $ 75, b = 14%C.P. = R × 100 b - a
Correct Option: B
Let the CP of cycle be $ y
S.P. = 108y 100 108y + 75 = 114y 100 100
⇒ 108y + 7500 = 114y
⇒ 114y – 108y = 7500
⇒ 6y = 7500⇒ y = 7500 = $ 1250 6
We can find required answer with the help of given formula :
Here, a = 8%, R= $ 75, b = 14%C.P. = R × 100 b - a C.P. = 75 × 100 14 - 8 ⇒ C.P. = 7500 = $ 1250 6
- A book vendor sold a book at a loss of 20%. Had he sold it for $ 108 more, he would have earned a profit of 30%. Find the cost price of the book?
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If the cost price of the book be $ y, then
According to question ,∴ y × ( 100 - 20 ) + 108 = y × ( 100 + 30 ) 100 100 ⇒ 13y - 4y = 108 10 5 ⇒ 13y -8y = 108 10 ⇒ 5y = 108 ⇒ y = $ 216 10
Using the given formula :
Here, a = 20%, R = $ 108, b = 30%C.P. = R × 100 b + a
Correct Option: A
If the cost price of the book be $ y, then
According to question ,∴ y × ( 100 - 20 ) + 108 = y × ( 100 + 30 ) 100 100 ⇒ 13y - 4y = 108 10 5 ⇒ 13y -8y = 108 10 ⇒ 5y = 108 ⇒ y = $ 216 10
Using the given formula :
Here, a = 20%, R = $ 108, b = 30%C.P. = R × 100 b + a C.P. = 108 × 100 30 + 20 C.P. = 10800 = $ 216 50
- If an article is sold at 5% gain instead of 5% loss, the man gains $ 5 more. Find the cost price of that article
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Let the C.P. be 100% .
∴ (5% + 5%) = 5 [Being 5% gain]
⇒ 10% = 51 % = 5 10 100 % = 5 × 100 = $ 50 10
We can find required answer with the help of given formula :
Here, a = 5%, R = $ 5, b = 5%C.P. = R × 100 b + a
Correct Option: C
Let the C.P. be 100% .
∴ (5% + 5%) = 5 [Being 5% gain]
⇒ 10% = 51 % = 5 10 100 % = 5 × 100 = $ 50 10
We can find required answer with the help of given formula :
Here, a = 5%, R = $ 5, b = 5%C.P. = R × 100 b + a C.P. = 5 × 100 = $ 50 5 + 5
