A shopkeeper buys an article for ₹ 450. He marks it at 20% above the cost price. Find :

(i) the marked price of the article.

(ii) the selling price, if he sells the article at 10 percent discount.

(iii) the percentage discount given by him, if he sells the article for ₹ 496.80.

(i) Given:

C.P. of an article = ₹ 450.

M.P. of the article = 20% above the C.P.

= C.P. + 20% of C.P.

= ₹ $450 + \dfrac{20}{100} \times 450$

= ₹ $450 + \dfrac{1}{5} \times 450$

= ₹ $450 + \dfrac{450}{5}$

= ₹ $450 + 90$

= ₹ $540$

Hence, M.P. of the article = ₹ $540$.

(ii) M.P. of the article = ₹ $540$

Discount = 10 %

As we know,

$\text{Discount \%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow 10 = \dfrac{\text{Discount}}{540} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{10 \times 540}{100}\\[1em] = \dfrac{5400}{100}\\[1em] = 54$

And

$\text{Discount = M.P. - S.P}\\[1em] \Rightarrow 54 = 540 - \text{S.P}\\[1em] \Rightarrow \text{S.P} = 540 - 54\\[1em] \Rightarrow \text{S.P} = ₹ 486$

Hence, S.P. of the article = ₹ 486.

(iii) When M.P. of the article = ₹ 540

S.P. of the article = ₹ 496.80

As we know ,

$\text{Discount = M.P. - S.P.}\\[1em] \text{Discount} = 540 - 496.80\\[1em] \text{Discount} = ₹ 43.2$

And,

$\text{Discount\%} = \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em] \Rightarrow\text{Discount\%} = \dfrac{43.2}{540} \times 100\\[1em] = \dfrac{4320}{540}\%\\[1em] = 8\%$

If S.P. of the article is ₹ 496.80, then the percentage discount is 8%.