Question

If the SP of 8 pens and CP of 10 pens are equal, find the profit or loss per cent.​

Answer 1

Given :

• SP and CP

To Find :

• Profit or loss percent

Solution :

Let the CP of one pen = rs. x

$\therefore \rm \: CP \: of \: 10 \: pens = rs.10x$

• According to question S.P. of 8 pens = rs. 10x

$\therefore \rm \: SP \: of \: 1 \: pen \: = \: rs. \dfrac{10x}{8}$

$\tt \: since \: \dfrac{10x}{8} > x \\ \therefore \tt \: SP > CP$

• So, there will be profit in the transaction.

$\rm \therefore \: Profit = \dfrac{10x}{8} - x \\ = \dfrac{10x - 8x}{8} \\ = \dfrac{2x}{8} \\ = \bf \dfrac{x}{4}$

$\tt \small \therefore \: Profit \: per \: cent \: = \dfrac{profit \: in \: 1pen}{CP \: of \: 1pen} \times100$

$\tt = \dfrac{ \dfrac{x}{4} }{x} \times100\% \\ \\ = \tt\frac{x}{4} \times \frac{1}{x} \times100\% \\ \\ \tt = 25\%$

Alternatively,

• According to question,

• SP of 8 pens = C.P of 10 pens
• or, 8 × SP = 10 × CP
• $\large\rm \: or, \dfrac{SP}{CP} = \frac{10}{8}$
• $\small\rm \: or, SP = \dfrac{10}{8} \times CP$

$\small \bf \therefore \: Profit \: per \: cent \: = \dfrac{profit}{CP} \times100\%$

• $\sf = \dfrac{sp \: - \: cp}{100} \times \: 100\% \\ \\ = \tt\dfrac{ \dfrac{10}{8}cp - cp }{cp} \times100\% \\ \\ = \tt \dfrac{ \frac{2}{8}cp }{cp} \times100\% \\ \\ \tt = \dfrac{2}{8} \times100\% \\ \\ \tt = 25\%$

$\bf\therefore \: Profit \: per \: cent = 25\%$