The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on the set of the shirt and trousers is 30%, the discount offered on the trousers is = ?

The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on the set of the shirt and trousers is 30%, the discount offered on the trousers is = ? Correct Answer 25%

Let the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively.
Let the discount offered on trousers be y%
Then, Selling price of shirt
$$\eqalign{ & = 60\% {\text{ of Rs}}{\text{. }}x \cr & = {\text{Rs}}\left( {\frac{{60}}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{3x}}{5} \cr & {\text{Selling price of trousers}} \cr & = \left( {100 - y} \right)\% {\text{ of Rs}}{\text{. }}2x \cr & = {\text{Rs}}.\left \cr & = {\text{Rs}}.\left \cr} $$
Combined Selling price of shirt and trousers
$$\eqalign{ & = 70\% {\text{ of Rs}}{\text{.}}\left( {x + 2x} \right) \cr & = {\text{Rs}}.\left( {\frac{{70}}{{100}} \times 3x} \right) \cr & = {\text{Rs}}.\frac{{21x}}{{10}} \cr & \therefore \frac{{3x}}{5} + \frac{{\left( {100 - y} \right)x}}{{50}} = \frac{{21x}}{{10}} \cr & \Rightarrow \frac{{130 - y}}{{50}} = \frac{{21}}{{10}} \cr & \Rightarrow 1300 - 10y = 1050 \cr & \Rightarrow y = 25 \cr} $$