Question

By selling pen for rs. 165, Mukti gains 10percent .if she had sold it for rs.157.50 what percent she have lost or gained

Answer 1

mukit gains lost by selling pen

Answer 2

Mukti gained 10%
$\frac{110}{100} \: of \: pen \: = \: 165 \\ purchase \: price = \frac{165 \times 100}{100} \\ if \: she \: had \: sold \: for \: rupees157.50 \\ gain \: or \: loss \: \% \: will \: be \: = 157.50 = 7.50 \\ percent \: of \: gain = \frac{75}{150} \times 100 \\ = \frac{75}{150} \times 100 = 5\%$

Or you can do it in other way:

$selling \: price \: of \: pen \\ when \: gain \: 10\% = 165 \\ actual \: price \: of \: pen \: = 165 \times \frac{100}{110} = 150 \\ now \: she \: had \: sold \: for \: 157.50 \\ gain \: = 157.50 - 150 = 7.50 \\ gain \: percent = \frac{75}{150} \times 100 = 5\%$
Hope it is correct.. ☺ ☺ ☺