Question

On selling an article for ₹144 a man loses 10%. At what price should he sell it to gain 10% ?

(a) ₹158.40
(b) ₹172.80
(c) ₹176
(d) ₹192

Answer 1

Let the CP of an article be x.

SP of the article = ₹144
Loss = 10%

Therefore, CP is more than SP.

Now, Loss = CP − SP and Loss = Loss percent × CP

$$\begin{gathered} \mathrm{Thus},\mathrm{CP}-\mathrm{SP}=\mathrm{Loss}\mathrm{percent}\times \mathrm{CP} \\ \Rightarrow x-144=\frac{10}{100}\times x \\ \Rightarrow x-144=\frac{1}{10}\times x \\ \Rightarrow 10x-1440=x \\ \Rightarrow 10x-x=1440 \\ \Rightarrow 9x=1440 \\ \Rightarrow x=\frac{1440}{9} \\ \Rightarrow x=160 \end{gathered}$$

Therefore, CP of the article = ₹160

Now, in order to gain 10%, let the new SP be y.

Gain = Gain percent × CP
= $\frac{10}{100}\times 160$
= ₹16

SP = CP + Gain
= ₹160 + ₹16
= ₹176

Hence, the correct option is (c).