Question

A man sold two bicycles for ₹6000 each, gaining 20% on the one and losing 20% on the other. Find his gain or loss per cent on the whole transaction.
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Answer 1

Your question:-

$\longrightarrow$A man sold two cycles for rs 6000 each. Gaining 20 % on one and losing 20 % on other. Find his gain or loss percentage on the whole transaction?

Solution:-

$\longmapsto$Total selling price = 12000

Cost price of first cycle be $\sf CP_1$

C.P of second cycle be$\sf CP_2$

Then,

➥For first cycle

6000 = CP1(1 + 20/100)

6000 = CP1(6/5)

CP1 = 1000×5 = 5000

➥For Second cycle

6000 = CP1(1 - 20/100)

6000 = CP1(4/5)

CP1 = 1500×5 = 7500

Total CP = 7500 + 5000 = 12500

Loss %

= [(Total CP - Total SP) / Total CP] ×100

= [(6250-6000)/6250]*100

= (250/6250)*100

=04*100

= 4%

There is loss of 4% in whole transaction

Answer 2

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

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

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

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

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.

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

$\to \dfrac {500}{12500} × 100 \% = 4\%.$

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