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.

Answer 1

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%