A shopkeeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.

Given:

M.P. of the goods = 30% above the C.P.

Let the C.P. be ₹ $100$.

M.P. = C.P. + 30% of C.P.

= $100 + \dfrac{30}{100} \times 100$

= $100 + \dfrac{30}{\cancel{100}} \times \cancel{100}$

= $100 + 30$

= $130$

So, M.P. of the goods = ₹ $130$

Discount % = 10%

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100 \\[1em] \Rightarrow 10 = \dfrac{\text{Discount}}{130} \times 100 \\[1em] \Rightarrow \text{Discount} = \dfrac{10 \times 130}{100}\\[1em] = \dfrac{1300}{100}\\[1em] = 13$

Now,

$\text{Discount = M.P. - S.P.} \\[1em] \Rightarrow 13 = 130 - \text{S.P.} \\[1em] \Rightarrow \text{S.P.} = 130 - 13 \\[1em] = 117$

Hence, S.P. of the goods = ₹ $117$

C.P. of the goods = ₹ 100

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

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \text{Gain} = 117 - 100 \\[1em] \Rightarrow \text{Gain} = 17$

And

$\text{Gain\%} = \dfrac{\text{Gain}}{\text{C.P.}} \times 100\%\\[1em] \Rightarrow\text{Gain\%} = \dfrac{17}{100} \times 100\%\\[1em] = \dfrac{17}{\cancel{100}} \times \cancel{100}\%\\[1em] = 17\%$

Hence, Gain percent = 17%