Question

A shopkeeper sold two fans for ​₹ 1140 each. On one he gains 14%, while on the other he loses 5%. Calculate his gain or loss per cent in the whole transaction.

Answer 1

SP of first fan = ₹1,140
Gain = 14%
Let the CP of first fan be ₹x.
CP = SP − Gain
$$\begin{gathered} \Rightarrow x=1140-\frac{14}{100}x \\ \Rightarrow x+\frac{14}{100}x=1140 \\ \Rightarrow \frac{114}{100}x=1140 \\ \Rightarrow x=1000 \end{gathered}$$
∴ CP of first fan = ₹1,000
SP of second fan = ₹1,140
Loss = 5%
Let the CP of second fan be ₹y.
CP = Loss + SP
$$\begin{gathered} \Rightarrow y=\frac{5}{100}y+1140 \\ \Rightarrow y-\frac{5}{100}y=1140 \\ \Rightarrow \frac{95}{100}y=1140 \\ \Rightarrow y=1200 \end{gathered}$$
∴ CP of second fan = ₹1,200
Total CP of two fans = CP of first fan + CP of second fan = ₹1,000 + ₹1,200 = ₹2,200
Total SP of two fans = SP of first fan + SP of second fan = ₹1,140 + ₹1,140 = ₹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = ₹2,280 − ₹2,200 = ₹80
∴ Gain% on whole transaction$=\frac{\mathrm{Gain}}{\mathrm{Total}\mathrm{CP}\mathrm{of}\mathrm{two}\mathrm{fans}}\times 100\%=\frac{80}{2200}\times 100\%=3.64\%$