By selling a sofa set for ₹ 2,500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa set for ₹ 3,150.

Given:

S.P. of sofa set = ₹ 2,500

Loss % = 20 %

Let C.P. = $₹x$.

$\text{Loss \%} = \dfrac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$\Rightarrow 20 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{20 \times x}{100}\\[1em] = \dfrac{x}{5}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{5} = x - 2,500\\[1em] \Rightarrow 2,500 = x - \dfrac{x}{5}\\[1em] \Rightarrow 2,500 = \dfrac{5x}{5} - \dfrac{x}{5}\\[1em] \Rightarrow 2,500 = \dfrac{(5x - x)}{5} \\[1em] \Rightarrow 2,500 = \dfrac{4x}{5}\\[1em] \Rightarrow x = \dfrac{2,500 \times 5}{4}\\[1em] \Rightarrow x = \dfrac{12,500}{4}\\[1em] \Rightarrow x = 3,125$

When C.P. = ₹ 3,125

New S.P. = ₹ 3,150

(∵ When S.P. is greater than C.P., means sofa set will be sold at a profit.)

Profit = S.P. - C.P.

= ₹ 3,150 - ₹ 3,125

= ₹ 25

$\text{Profit \%} = \dfrac{\text{Profit}}{\text{C.P.}} \times 100\%\\[1em] = \dfrac{25}{3125} \times 100\%\\[1em] = \dfrac{1}{125} \times 100\%\\[1em] = \dfrac{100}{125}\%\\[1em] = 0.8\%$

If the man sells the same sofa set for ₹ 3,150, profit % = 0.8%.