**Question:**

*Tick (✓) the correct answer:*

A man sold two chairs for Rs 500 each. On one he gains 20% and on the other he loses 12%. His net gain or loss per cent is

(a) 1.5% gain

(b) 2% gain

(c) 1.5% loss

(d) 2% loss

**Solution:**

(a) 1.5% gain

SP of the first chair $=$ Rs 500

Gain percentage $=20 \%$

$\therefore \mathrm{CP}$ of the first chair $=\left\{\frac{100}{(100+\text { gain } \%)} \times \mathrm{SP}\right\}$

$=$ Rs. $\left\{\frac{100}{(100+20)} \times 500\right\}$

$=$ Rs. $\left(\frac{100}{120} \times 500\right)$

$=$ Rs. $416.67$

SP of the second chair $=$ Rs. 500

Loss percentage $=12 \%$

$\therefore \mathrm{CP}$ of the second chair $=\left\{\frac{100}{(100-\text { loss } \%)} \times \mathrm{SP}\right\}$

$=$ Rs. $\left\{\frac{100}{(100-12)} \times 500\right\}$

$=$ Rs. $\left(\frac{100}{88} \times 500\right)$

$=$ Rs. $568.18$

Total CP of the two chairs $=$ Rs. $(416.67+568.18)$

$\quad=$ Rs. $984.85$

Total SP of the two chairs $=$ Rs. $(500 \times 2)$

$\quad=$ Rs. 1000

Since SP $>$ CP, there is a gain in the whole transaction.

Now, gain $=$ Rs. $(1000-984.85)$

$=R s .15 .15$

$\therefore$ Gain percentage $=\left(\frac{\text { gain }}{\text { CP }} \times 100\right) \%$

$=\left(\frac{15.15}{984.85} \times 100\right) \%$

$=1.5 \%$