A book shopkeeper gives a discount of 30% on a book and makes a profit of 20% . If the book shopkeeper had given a discount of Rs. 400, he would have incurred a loss of 20% . Find the marked price (in Rs) of the book.
A book shopkeeper gives a discount of 30% on a book and makes a profit of 20% . If the book shopkeeper had given a discount of Rs. 400, he would have incurred a loss of 20% . Find the marked price (in Rs) of the book.
The correct option is A 750
Let the marked price of the book be x. Selling Price (SP) after discount of 30%
=x(1−30100)=7x10
It is known that there is a profit of 20% of SP 7x10
∴CP=7x10(100100+20)=7x12.
New SP=x-400 and on this new SP there is a loss of 20%.
⇒7x12(1−20100)=x−400
⇒7x15=x−400⇒400=x−7x15
⇒9x15=400⇒x=750
Shortcut- Using the reverse Gear Approach
Always start with a middle answer option
Assuming 750 as the right answer option.
If he gives a discount of 30% then the selling price will be 750 - 225=525, with which he is able to make a profit of 20%.
Thus, cost price will be =(5251.20)=437.5
Again if he had given a discount of 400 Rs. He would have sold the book at 750 - 400=350 he incurred a loss of 20% or (3500.8)=437.5 hence that is the correct option.
750
Let the marked price of the book be x.
Selling Price (SP) after discount of 30%
=x(1−30100)=7x10
It is known that there is a profit of 20% of SP 7x10
∴CP=7x10(100100+20)=7x12.
New SP=x-400 and on this new SP there is a loss of 20%.
⇒7x12(1−20100)=x−400
⇒7x15=x−400⇒400=x−7x15
⇒9x15=400⇒x=750
Shortcut- Using the reverse Gear Approach
Always start with a middle answer option
Assuming 750 as the right answer option.
If he gives a discount of 30% then the selling price will be 750 - 225=525, with which he is able to make a profit of 20%.
Thus, cost price will be =(5251.20)=437.5
Again if he had given a discount of 400 Rs. He would have sold the book at 750 - 400=350 he incurred a loss of 20% or (3500.8)=437.5 hence that is the correct option.
