Question

Luxmi sold two sarees for ₹ 1980 each. On one, she lost 10%, while on the other she gained 10%. Find her gain or loss per cent in the whole transaction.

Answer 1

SP of first saree = ₹1,980
Loss = 10%
Let the CP of first saree be ₹x.
CP = Loss + SP
$$\begin{gathered} \Rightarrow \frac{10}{100}\times x+1980=x \\ \Rightarrow x-\frac{{\displaystyle 10}}{{\displaystyle 100}}x=1980 \\ \Rightarrow \frac{90}{100}x=1980 \\ \Rightarrow x=2200 \end{gathered}$$
∴ CP of first saree = ₹2,200
SP of second saree = ₹1,980
Gain = 10%
Let the CP of second saree be ₹y.
CP = SP − Gain
$$\begin{gathered} \Rightarrow 1980-\frac{10}{100}\times y=y \\ \Rightarrow 1980-\frac{y}{10}=y \\ \Rightarrow y+\frac{y}{10}=1980 \\ \Rightarrow \frac{11y}{10}=1980 \\ \Rightarrow y=1800 \end{gathered}$$
∴ CP of second saree = ₹1,800
Total CP of two sarees = CP of first saree + CP of second saree = ₹2,200 + ₹1,800 = ₹4,000
Total SP of two sarees = SP of first saree + SP of second saree = ₹1,980 + ₹1,980 = ₹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = ₹4,000 − ₹3,960 = ₹40
∴ Loss% in the whole transaction$=\frac{\mathrm{Loss}}{\mathrm{Total}\mathrm{CP}\mathrm{of}\mathrm{two}\mathrm{sarees}}\times 100\%=\frac{40}{4000}\times 100\%=1\%$