The cost price of an article is ₹ 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.

Given:

M.P. of the article = 25% above the C.P.

The C.P. of the article = ₹ 2,400.

M.P. = C.P. + 25% of C.P.

= $2,400 + \dfrac{25}{100} \times 2,400$

= $2,400 + \dfrac{1}{4} \times 2,400$

= $2,400 + \dfrac{2,400}{4}$

= $2,400 + 600$

= $3,000$

So, M.P. of the goods = ₹ $3,000$

Discount % = 15%

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100 \\[1em] \Rightarrow 15 = \dfrac{\text{Discount}}{3000} \times 100 \\[1em] \Rightarrow \text{Discount} = \dfrac{15 \times 3,000}{100}\\[1em] = \dfrac{45,000}{100}\\[1em] = 450$

Now,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 450 = 3,000 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 3,000 - 450\\[1em] = 2,550$

Hence, S.P. of the goods = ₹ $2,550$

C.P. of the goods = ₹ $2,400$

($\because$ S.P. is greater than C.P., means goods are sold at a gain.)

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \text{Gain} = 2,550 - 2,400 \\[1em] \Rightarrow \text{Gain} = 150$

And

$\text{Gain\%} = \dfrac{\text{Gain}}{\text{C.P.}} \times 100\%\\[1em] \Rightarrow\text{Gain\%} = \dfrac{150}{2400} \times 100\%\\[1em] = \dfrac{15000}{2400} \%\\[1em] = 6.25\%$

Hence, Gain = ₹ 150 and Gain percent = 6.25%