Question

a man sold two bycycle for 6000 each,gaining 20% on one and losing 20% on other.find his gain or loss percent on the whole transaction

Answer 1

$\fbox \purple {AnSwEr:-}$

$\mathbb{First \: Bicycle:-}$

$S.P. \: = \: rs. \: 6000, \: Gain\% \: = \: 20\%. \\ C.P. \: = \: \frac{100}{(100 \: + \: Gain\%} \times\ S.P. \: \\ = \: rs. \: \ \frac{100}{(100 \: + \: 20)} \times\ 6000 \\ = \: rs. \: \: \frac{100}{120} \times \: 6000 \: = \: rs. \: 5000.$

$\mathbb{Second \: Bicycle:-}$

$S.P. \: = \: rs. \: 6000, \: Loss\% \: = \: 20\%. \\ C.P. \: = \: \frac{100}{(100 \: - \: Loss\%)} \times\ S.P. \\ = \: rs. \: \times \frac{100}{(100 \: - \: 20)} \: \times\ 6000 \\ = \: rs. \: \: \frac{100}{80} \: \times\ 6000 \: = \: rs. \: 7500.$

Total C.P. of 2 bicycles = rs. (5000 + 7500) = rs. 12500.

Total S.P. of two bicycles = rs. (6000 × 2) = rs. 12000.

Since S.P. < C.P., so there is a loss.

Loss = rs. (12500 - 12000) = 500.

∴ Loss% = $\frac {Loss}{C.P.}\ ×\ 100\ %$

500/12500 × 100 % = 4%.

Hence, the man loss 4% on the whole transaction.