A man sells a radio set for ₹ 605 and gains 10%. At what price should he sell another radio of the same kind in order to gain 16% ?

Given:

S.P. of radio set = ₹ 605

Gain % = 10 %

Let C.P. = $₹x$.

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

Putting the values, we get

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

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{10} = 605 - x\\[1em] \Rightarrow 605 = \dfrac{x}{10} + x\\[1em] \Rightarrow 605 = \dfrac{10x}{10} + \dfrac{x}{10}\\[1em] \Rightarrow 605 = \dfrac{(10x + x)}{10} \\[1em] \Rightarrow 605 = \dfrac{11x}{10}\\[1em] \Rightarrow x = \dfrac{10 \times 605}{11}\\[1em] \Rightarrow x = \dfrac{6,050}{11}\\[1em] \Rightarrow x = 550$

Hence, C.P. = ₹ 550

Profit % = 16 %

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

Putting the values, we get

$\Rightarrow 16 = \dfrac{\text{Profit}}{550} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{16 \times 550}{100}\\[1em] = \dfrac{8800}{100}\\[1em] = 88$

And,

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

Putting all the values, we get

$\Rightarrow 88 = \text{S.P.} - 550\\[1em] \Rightarrow \text{S.P.} = 88 + 550\\[1em] = 638$

The man should sell the other radio for ₹ 638 in order to make a profit of 16%.