A box is sold for ₹ 18 at a loss of 10%. When sold at a profit of 15%; its S.P. will be :

1. ₹ 17

2. ₹ 19

3. ₹ 21

4. ₹ 23

Given:

S.P. = ₹ 18

Loss % = 10%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 10 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{10 \times x}{100}\\[1em] = \dfrac{x}{10}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{10} = x - 18\\[1em] \Rightarrow 18 = x - \dfrac{x}{10} \\[1em] \Rightarrow 18 = \dfrac{10x}{10} - \dfrac{x}{10}\\[1em] \Rightarrow 18 = \dfrac{(10x - x)}{10} \\[1em] \Rightarrow 18 = \dfrac{9x}{10}\\[1em] \Rightarrow x = \dfrac{18 \times 10}{9}\\[1em] \Rightarrow x = \dfrac{180}{9}\\[1em] \Rightarrow x = 20$

When C.P. = ₹ 20

Profit % = 15 %

$\text {Profit\%} = \dfrac{\text{Profit}}{\text{C.P.}}\times 100\\[1em] \Rightarrow\text {15} = \dfrac{\text{Profit}}{20}\times 100\\[1em] \Rightarrow\text{Profit} = \dfrac{15 \times 20}{100}\\[1em] \Rightarrow\text{Profit} = \dfrac{300}{100}\\[1em] \Rightarrow\text{Profit} = 3$

And,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 3 =\text{S.P.} - 20\\[1em] \Rightarrow \text{S.P.} = ₹ 20 + 3\\[1em] \Rightarrow \text{S.P.} = ₹ 23$

Hence, option 4 is the correct option.