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Question
A shopkeeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
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Solution
Given:
M.P. of the goods = 30% above the C.P.
Let the C.P. be ₹ 100.
M.P. = C.P. + 30% of C.P.
= `100 + 30/100 xx 100`
= `100 + 30/(cancel(100)) xx cancel(100)`
= 100 + 30
= 130
So, M.P. of the goods = ₹ 130
Discount % = 10%
Discount% = `("Discount")/("M. P.") xx 100`
= `10 = ("Discount")/130 xx 100`
= Discount = `(10 xx 130)/100`
= `1300/100`
= 13
Now,
Discount = M.P. - S.P.
⇒ 13 = 130 − S.P.
⇒ S.P. = 130 − 13
= 117
Hence, S.P. of the goods = ₹ 117
C.P. of the goods = ₹ 100
(∵ S.P. is greater than C.P., means goods are sold at a gain.)
Gain = S.P. − C.P.
⇒ Gain = 117 − 100
⇒ Gain = 17
And
Gain% = `("Gain")/("C. P.") xx 100%`
⇒ Gain% = `17/100 xx 100%`
= `17/cancel(100) xx cancel(100%)`
= 17%
Hence, Gain percent = 17%
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