Question

A garment retailer gives a percentage discount on formal coats, which is equal to his profit percentage on formal coats. The cost price to marked price ratio is 3:5 on formal coats. If selling price of formal coat is RS. 1200.what is the cost price of one formal coat?​

Answer 1

Given:

A garment retailer gives a percentage discount on formal coats, which is equal to his profit percentage on formal coats.

The cost price to marked price ratio is 3:5 on formal coats.

If selling price of the formal coat is RS. 1200.

To find:

What is the cost price of one formal coat?​

Formulas to be used:

$\boxed{\bold{Discount \% = \frac{M.P. - S.P.}{M.P.} \times 100 }} \\\\\boxed{\bold{Profit \% = \frac{S.P. - C.P. }{C.P. } \times 100 }}$

Solution:

Let's assume,

"3x" → represents the cost price of the formal coats

"5x" → represents the marked price of the formal coats

The S.P. of the formal coat = Rs. 1200

We are given that,

Discount% = Profit%

∴ $\frac{M.P. - S.P.}{M.P.} \times 100 }} = \frac{S.P. - C.P. }{C.P. } \times 100$

on substituting M.P. = 5x, C.P. = 3x & S.P. = 1200, we get

$\implies \frac{5x - 1200}{5x} \times 100 }} = \frac{1200 - 3x }{3x } \times 100$

$\implies \frac{5x - 1200}{5} = \frac{1200 - 3x }{3 }$

$\implies 3(5x - 1200) = 5(1200 - 3x)$

$\implies 15x - 3600 = 6000 - 15x$

$\implies 15x + 15x = 6000 + 3600$

$\implies 30x = 9600$

$\implies x =\frac{9600}{30}$

$\implies \bold{x = 320}$

∴ C.P. = 3x = 3 × 320 = Rs. 960

Thus, the cost price of one formal coat is → Rs. 960.

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