**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.

**Solution:**

SP of first fan $=₹ 1,140$

Gain $=14 \%$

Let the CP of first fan be ₹ $x$.

CP $=$ SP - Gain

$\Rightarrow x=1140-\frac{14}{100} x$

$\Rightarrow x+\frac{14}{100} x=1140$

$\Rightarrow \frac{114}{100} x=1140$

$\Rightarrow x=1000$

$\therefore$ 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

$\Rightarrow y=\frac{5}{100} y+1140$

$\Rightarrow y-\frac{5}{100} y=1140$

$\Rightarrow \frac{95}{100} y=1140$

$\Rightarrow y=1200$

∴ 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

$\therefore$ Gain $\%$ on whole transaction $=\frac{\text { Gain }}{\text { Total } \text { CP of two fans }} \times 100 \%=\frac{80}{2200} \times 100 \%=3.64 \%$

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