**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.

**Solution:**

SP of first saree $=₹ 1,980$

Loss $=10 \%$

Let the CP of first saree be ₹ $x .$

CP $=$ Loss $+$ SP

$\Rightarrow \frac{10}{100} \times x+1980=x$

$\Rightarrow x-\frac{10}{100} x=1980$

$\Rightarrow \frac{90}{100} x=1980$

$\Rightarrow x=2200$

$\therefore$ 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

$\Rightarrow 1980-\frac{10}{100} \times y=y$

$\Rightarrow 1980-\frac{y}{10}=y$

$\Rightarrow y+\frac{y}{10}=1980$

$\Rightarrow \frac{11 y}{10}=1980$

$\Rightarrow y=1800$

∴ 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

$\therefore$ Loss $\%$ in the whole transaction $=\frac{\text { Loss }}{\text { Total CP of two sares }} \times 100 \%=\frac{40}{4000} \times 100 \%=1 \%$