Question

Velan sells a bicycle for 21900 and his loss is 5% of his cost price. If he wants to gain 15%
profit, then find the new selling price.​

Answer 1

Given :

• When bicycle is sells at 21900 , loss = 5%

To find :

Selling price for gain 15% profit

Formula used :

• Profit = S.P. - C.P.
• Loss = C.P. - S.P.
• Loss% = (Loss × 100)/C.P.
• Profit% = (Profit×100)/C.P.

Solution :

First of all we need to find cost price of bicycle.

$\sf \implies \: Loss\% = \: \dfrac{ C.P. - S.P. \: }{C.P.} \times 100$

$\sf \implies \: 5 \: = \: \dfrac{ C.P. - S.P. \: }{C.P.} \times 100$

$\sf \implies \:5 \times C.P. \: = \: (C.P. - S.P. )\times 100$

$\sf \implies \:5 \times C.P. \: = \: (C.P. - \: 21900 ) \: \times 100$

$\sf \implies \:5 C.P. \: = \:(C.P.\: \times 100 ) - \: (21900 \times 100) \:$

$\sf \implies \:5 C.P. \: = \:100C.P.\: - 2190000 \:$

$\sf \implies \: 100C.P.\: - \:5 C.P. = \: 2190000 \:$

$\sf \implies \: 95C.P.\: = \: 2190000 \:$

$\sf \implies \:C.P.\: = \: \dfrac{2190000}{95} \:$

$\sf \implies \:C.P.\: = \: 23502.63$

Now , we know the cost price of bicycle. Now we need to find out the selling price for bicycle to gain 15% profit

$\sf \implies \: Profit\% = \: \dfrac{ S.P._{2} - C.P. \: }{C.P.} \times 100$

$\sf \implies \: 15 = \: \dfrac{ S.P._{2} - C.P. \: }{C.P.} \times 100$

$\sf \implies \: 15 \: \times \:C.P. = \: (S.P._{2} - C.P. ) \: \times 100$

$\sf \implies \: 15 \: \times \:C.P. = \: (S.P._{2} \times 100) - ( C.P.\: \times 100 )$

$\sf \implies \: 15 \: \:C.P. = \: 100S.P._{2} - 100 C.P.\:$

$\sf \implies \: 15 \:C.P. + \: 100 C.P.\: = \: 100S.P._{2}$

$\sf \implies \: 115C.P.\: = \: 100S.P._{2}$

$\sf \implies \: \: S.P._{2} = \dfrac{115C.P.\:}{100}$

$\sf \implies \: \: S.P._{2} = \dfrac{115 \times 23052.63\:}{100}$

$\sf \implies \: \: S.P._{2} = 26150.52$

ANSWER :

New Selling price = 26150.52