**Question:**

A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.

**Solution:**

Let $R s x$ be the CP.

Gain $_{1}$ percentage $=\left(\frac{\operatorname{gain}_{1}}{\mathrm{CP}} \times 100\right) \%$

$\Rightarrow 15=\frac{\text { gain }_{1}}{x} \times 100$

$\Rightarrow$ Gain $_{1}=$ Rs $\frac{15 x}{100}$

Again, gain $_{2}$ percentage $=\left(\frac{\mathrm{gain}_{2}}{\mathrm{CP}} \times 100\right) \%$

$\Rightarrow 8=\frac{\text { gain }_{2}}{x} \times 100$

$\Rightarrow$ Gain $_{2}=$ Rs $\frac{8 x}{100}$

According to the question, we have:

Gain $_{1}-$ gain $_{2}=56$

$\Rightarrow \frac{15 x}{100}-\frac{8 x}{100}=56$

$\Rightarrow \frac{7 x}{100}=56$

$\Rightarrow 7 x=5600$

$\Rightarrow x=800$

Hence, the CP of the chair is Rs 800 .