If John sells his bicycle for ₹ 637, he will suffer a loss of 9%. For how much should it be sold if he desires a profit of 5% ?

Given:

S.P. of bicycle = ₹ 637

Loss % = 9%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 9 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{9 \times x}{100}\\[1em] = \dfrac{9x}{100}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{9x}{100} = x - 637\\[1em] \Rightarrow 637 = x - \dfrac{9x}{100}\\[1em] \Rightarrow 637 = \dfrac{100x}{100} - \dfrac{9x}{100}\\[1em] \Rightarrow 637 = \dfrac{(100x - 9x)}{100} \\[1em] \Rightarrow 637 = \dfrac{91x}{100}\\[1em] \Rightarrow x = \dfrac{100 \times 637}{91}\\[1em] \Rightarrow x = \dfrac{63,700}{91}\\[1em] \Rightarrow x = 700$

Hence, C.P. = ₹ 700

Profit % = 5 %

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

Putting the values, we get

$\Rightarrow 5 = \dfrac{\text{Profit}}{700} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{5 \times 700}{100}\\[1em] = \dfrac{3500}{100}\\[1em] = 35$

And,

$\text{Profit} = \text{S.P. - C.P.}$

Putting all the values, we get

$\Rightarrow 35 = \text{S.P.} - 700\\[1em] \Rightarrow \text{S.P.} = 35 + 700\\[1em] = 735$

John should sell his bicycle for ₹ 735 to make a profit of 5%.