At 12% discount, the selling price of a pen is ₹ 13.20. Find its marked price. Also find the new selling price of the pen, if it is sold at 5% discount.

Given:

S.P. of the pen = ₹ 13.20

Discount % = 12%

Let the M.P. of the pen = ₹ $x$.

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 13.20$

And,

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 12 = \dfrac{(x - 13.20)}{x} \times 100\\[1em] \Rightarrow 12 \times x = (x - 13.20) \times 100\\[1em] \Rightarrow 12x = 100x - 1320\\[1em] \Rightarrow 1320 = 100x - 12x \\[1em] \Rightarrow 1320 = 88x \\[1em] \Rightarrow x = \dfrac{1320}{88} \\[1em] \Rightarrow x = 15$

Now, M.P. of the pen = ₹ 15

Discount% = 5 %

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 5 = \dfrac{\text{Discount}}{15}\times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{5 \times 15}{100}\\[1em] = \dfrac{75}{100}\\[1em] = 0.75$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 0.75 = 15 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 15 - 0.75\\[1em] \Rightarrow \text{S.P.} = 14.25$

Hence, M.P. of pen = ₹ 15 and new S.P. = ₹ 14.25