Raju sells a watch at 5% profit. Had he sold it for ₹ 24 more he would have gained 11%. Find the cost price of the watch.

Let C.P. of the watch be ₹ $x$.

Profit % = 5 %

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

Putting the values, we get

$5 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{5 \times x}{100}\\[1em] = \dfrac{x}{20}$

As we know,

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

Putting the values, we get

$\dfrac{x}{20} = \text{S.P.} - x\\[1em] \Rightarrow \text{S.P.} = \dfrac{x}{20} + x\\[1em] = \dfrac{x}{20} + \dfrac{20x}{20}\\[1em] = \dfrac{(x + 20x)}{20}\\[1em] = \dfrac{21x}{20}$

Given,

If S.P. was 24 more gain would have been 11%

New S.P. = $\dfrac{21x}{20} + 24$

New Profit = New S.P. - C.P.

$= \dfrac{21x}{20} + 24 - x \\[1em] = \dfrac{21x + 480 - 20x}{20} \\[1em] = \dfrac{x + 480}{20}$

New Profit % = 11 %

$\text{Profit\%} = \dfrac{\text{Profit}}{\text{C.P}}\times 100 \\[1em] \Rightarrow 11 = \dfrac{\dfrac{x + 480}{20}}{x} \times 100 \\[1em] \Rightarrow 11 = \dfrac{x + 480}{20x} \times 100 \\[1em] \Rightarrow 11 = \dfrac{x + 480}{x} \times 5 \\[1em] \Rightarrow 11x = 5x + 2400 \\[1em] \Rightarrow 11x - 5x = 2400 \\[1em] \Rightarrow 6x = 2400 \\[1em] \Rightarrow x = \dfrac{2400}{6} \\[1em] \Rightarrow x = 400$

Hence, cost price of watch = ₹ 400.