Question

The marked price of a shirt and trouser are in the ratio 1:2, the shopkeeper gives a 40% discount on the shirt. If the total discount of both is 30%, then the discount offered on trousers is
A. 15%
B. 20%
C. 25%
D. 30%

Answer 1

Hint: First we will assume that the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively and Let the discount offered on trousers be y%
If 40% discount is on the shirt it means its selling price will be \[(100-40)=60\%\] of the x
Selling price equals to \[\dfrac{60}{100}x\]
And similarly
If y% discount is on the trouser it means its selling price will be \[(100-y)\%\] of the 2x
Selling price equals to \[(\dfrac{100-y}{100})\times 2x\]
Now 30% is total discount so we can say that \[(\dfrac{30}{100})\times (x+2x)=\dfrac{60}{100}x+(\dfrac{100-y}{100})\times 2x\]
On simplifying we get the answer.

Complete step by step answer:
Given here the marked price of a shirt and trouser are in the ratio 1:2, and the shopkeeper gives a 40% discount on the shirt. If the total discount of both is 30%, then we have to calculate discount offered on trousers, so first assume we will assume that the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively and Let the discount offered on trousers be y%
One property we should know that if the discount of any item is a% it means its selling price will be (100-a) % of marked price.
Now If 40% discount is on the shirt it means its selling price will be \[(100-40)=60\%\]of the x
Selling price equals to \[\dfrac{60}{100}x\]
similarly
If y% discount is on the trouser it means its selling price will be \[(100-y)\%\] of the 2x
Selling price equals to \[(\dfrac{100-y}{100})\times 2x\]
Now it is given that 30% is total discount on total purchase so we can say that
\[(\dfrac{100-30}{100})\times (x+2x)\] will be the total selling price
And we can say that selling price of total product will be equals to sum of selling price of individual
So, we can write It in mathematical format as
\[(\dfrac{70}{100})\times (3x)=\dfrac{60}{100}x+(\dfrac{100-y}{100})\times 2x\]
On simplifying \[70\times (3)=60+(100-y)\times 2\], now further solving
\[210=60+(100-y)\times 2\] on solving gives \[150=(100-y)\times 2\]
Finally, \[y=25\]

Hence 25% is the discount offered on trousers.

Note: First of all, the marked price of trousers is Rs. 2x so consider it properly while applying formula most of the students take it as Rs. x only. One more mistake students can make is if the discount of any item is a% it means its selling price will be (100-a) % of marked price and not a% of marked price.