A man sold a radio set for ₹ 250 and gained one-ninth of its cost price. Find:

(i) its cost price;

(ii) the profit percent.

(i) Given:

S.P. of the radio set = ₹ 250

Gain = one-ninth of its C.P.

Let the C.P. be ₹ $x$.

Gain = $\dfrac{1}{9} \times x$

= $\dfrac{x}{9}$

As we know,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\dfrac{x}{9} = 250 - x\\[1em] \Rightarrow \dfrac{x}{9} + x = 250\\[1em] \Rightarrow \dfrac{x}{9} + \dfrac{9x}{9} = 250\\[1em] \Rightarrow \dfrac{(x + 9x)}{9} = 250\\[1em] \Rightarrow \dfrac{10x}{9} = 250\\[1em] \Rightarrow x = \dfrac{250 \times 9}{10} \\[1em] \Rightarrow x = \dfrac{2250}{10} \\[1em] \Rightarrow x = 225$

Hence, the cost price = ₹ 225.

(ii) Gain = one-ninth of its C.P.

= $\dfrac{1}{9} \times 225$

= $\dfrac{225}{9}$

= $25$

$\text{Gain\%} = \dfrac{\text{Gain}}{\text{C.P.}} \times 100\\[1em] \Rightarrow \text{Gain\%} = \dfrac{25}{225} \times 100\%\\[1em] = \dfrac{1}{9} \times 100\%\\[1em] = \dfrac{100}{9}\%\\[1em] = 11\dfrac{1}{9}\%$

Hence, the gain percent = $11\dfrac{1}{9}\%$.