Question

If the S.P. of Rs. 24 results in a $20\% $ discount on list price, what S.P. would result in a $30\% $ discount on list price?
A) Rs.18
B) Rs.20
C) Rs.21
D) Rs.27

Answer 1

Hint:
We can take the list price as x. Then the discounted money will be equal to the given percentage of x. Then we can find the selling price in terms of x and equate it with the given selling price. Then we can solve for x, using the value of x, we can find the discount of at $30\% $ discount. Then we can subtract it from the list price to get the required selling price.

Complete step by step solution:
Let x be the list price of the object.
For a $20\% $ discount on list price, the discount will be $20\% $ of x. So, we can write,
 ${D_1} = 20\% x$
On converting percentage into fraction, we get,
 $ \Rightarrow {D_1} = \dfrac{{20}}{{100}}x$
On cancelling the zeros, we get,
 $ \Rightarrow {D_1} = \dfrac{2}{{10}}x$
We know that selling price is given by subtracting the discount price from the list price.
 $ \Rightarrow {S_1} = x - {D_1}$
It is given that selling price is Rs. 24. On substitution, we get,
 $ \Rightarrow 24 = x - \dfrac{{2x}}{{10}}$
On taking the LCM, we get,
 $ \Rightarrow 24 = \dfrac{{10x - 2x}}{{10}}$
On simplification we get,
 $ \Rightarrow 24 = \dfrac{{8x}}{{10}}$
On cross multiplication, we get,
 $ \Rightarrow 8x = 24 \times 10$
On dividing throughout with 8, we get,
 $ \Rightarrow x = \dfrac{{24 \times 10}}{8}$
On simplification, we get,
 $ \Rightarrow x = 30$
Thus, the list price is Rs. 30.
Now we need to find the S.P when there is a $30\% $ discount on list price.
For a $30\% $ discount on list price, the discount will be $30\% $ of the list price. So, we can write,
 ${D_2} = 30\% x$
On converting percentage into fraction, we get,
 $ \Rightarrow {D_2} = \dfrac{{30}}{{100}}x$
On cancelling the zeros, we get,
 $ \Rightarrow {D_2} = \dfrac{3}{{10}}x$
On substituting the value of x, we get,
 $ \Rightarrow {D_2} = \dfrac{3}{{10}} \times 30$
On further simplification, we get,
 $ \Rightarrow {D_2} = 3 \times 3$
So, we have,
 $ \Rightarrow {D_2} = 9$
We know that selling price is given by subtracting the discount price from the list price.
 $ \Rightarrow {S_2} = x - {D_2}$
On substituting the values, we get,
 $ \Rightarrow {S_2} = 30 - 9$
On simplification we get,
 $ \Rightarrow {S_2} = 21$
So, the selling price when there is $30\% $ discount on list price is Rs. 21.
Therefore, the required solution is Rs.21.

So, the correct answer is option C.

Note:
Alternate solution is given by,
Let x be the list price of the object.
As the discount is $20\% $ , the selling price will be $80\% $ .
So, we can write,
 $ \Rightarrow {S_1} = 80\% x$ .
On substitution of simplification, we get,
 \[ \Rightarrow 24 = \dfrac{{80}}{{100}}x\]
On rearranging, we get,
 \[ \Rightarrow x = \dfrac{{24 \times 100}}{{80}}\]
On further simplification,
 \[ \Rightarrow x = 30\]
Now consider the case where discount is $30\% $
As the discount is $30\% $ , the selling price will be $70\% $ .
So, we can write,
 \[ \Rightarrow {S_2} = 70\% x\] .
On substitution of simplification, we get,
 \[ \Rightarrow {S_2} = \dfrac{{70}}{{100}} \times 30\]
On simplification, we get,
 $ \Rightarrow {S_2} = 21$
So, the selling price when there is $30\% $ discount on list price is Rs. 21.
Therefore, the required solution is Rs.21.