A shopkeeper earns a profit of 15% on selling a book at 15% discount on the printed price. The ratio of the cost price and the printed price of the book is:
- A20 : 23
- B23 : 20
- C23 : 17
- D17 : 23
Solution & Step-by-step Explanation
Let the Cost Price be CP and the Printed Price (Marked Price) be MP.
The relationship between Selling Price (SP), CP, and MP is given by:
SP=CP×(1+
100
Profit %
)=MP×(1−
100
Discount %
)
Given Profit %=15% and Discount %=15%:
CP×(1+
100
15
)=MP×(1−
100
15
)
CP×
100
115
=MP×
100
85
CP×115=MP×85
Now, finding the ratio of CP to MP:
MP
CP
=
115
85
=
23
17
Therefore, the ratio is 17:23.
The relationship between Selling Price (SP), CP, and MP is given by:
SP=CP×(1+
100
Profit %
)=MP×(1−
100
Discount %
)
Given Profit %=15% and Discount %=15%:
CP×(1+
100
15
)=MP×(1−
100
15
)
CP×
100
115
=MP×
100
85
CP×115=MP×85
Now, finding the ratio of CP to MP:
MP
CP
=
115
85
=
23
17
Therefore, the ratio is 17:23.