
A shopkeeper earns a profit of \[15\%\] after selling a book at $20\%$ discount on the printed price. Find the ratio of the cost price and the printed price of the book?
(a) $16:23$,
(b) $20:23$,
(c) $23:16$,
(d) $23:20$.
Answer
557.1k+ views
Hint: We start solving the problem by assigning the variables for the cost, printed and selling prices of the book. We then find the selling price of the book using the information that the shopkeeper sold $20\%$ less than the printed price of the book. We then use the information that shopkeeper got $15\%$ profit after selling and use the fact that $profit\%=\dfrac{selling\ price-\text{cost } price}{\operatorname{cost } price}\times 100$ to get the required ratio after making necessary calculations.
Complete step-by-step answer:
According to the problem, we have given that the shopkeeper earns a profit of \[15\%\] after selling a book at $20\%$ discount on the printed price. We need to find the ratio of the cost price and the printed price of the book.
Let us assume the cost price, printed price and the selling price be c, p and s.
According to the problem, we have given that the selling price is $20\%$ less than the printed price.
So, we get the selling price = $\left( 100-20 \right)\%$ of printed price.
$\Rightarrow $Selling price = $80\%$ of printed price.
We know that $x\%$ of y = $\dfrac{x}{100}\times y$.
$\Rightarrow s=\dfrac{80}{100}\times p$.
$\Rightarrow s=0.8p$---(1).
According to the problem, we are given that the shop keeper earned a profit of $15\%$ on selling the book at a price of $0.8p$.
We know that $profit\%=\dfrac{selling\ price-\text{cost } price}{\operatorname{cost} price}\times 100$.
So, we get $15\%=\dfrac{0.8p-c}{c}\times 100$.
$\Rightarrow 0.15=\dfrac{0.8p}{c}-1$.
$\Rightarrow 1.15=\dfrac{0.8p}{c}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{0.8}{1.15}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{80}{115}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{16}{23}$.
So, we have found the ratio of cost price and printed price of the book as $16:23$.
So, the correct answer is “Option (a)”.
Note: We can see that there are high chances of making mistakes while solving this problem. So, we need to solve each step properly in order to avoid the mistakes. We can also find the total amount profit gained by the shopkeeper after getting the ratio between cost price and the printed price, as we are taking all the values in terms of printed price. Similarly, we can also expect problems to find the selling price and price of the book.
Complete step-by-step answer:
According to the problem, we have given that the shopkeeper earns a profit of \[15\%\] after selling a book at $20\%$ discount on the printed price. We need to find the ratio of the cost price and the printed price of the book.
Let us assume the cost price, printed price and the selling price be c, p and s.
According to the problem, we have given that the selling price is $20\%$ less than the printed price.
So, we get the selling price = $\left( 100-20 \right)\%$ of printed price.
$\Rightarrow $Selling price = $80\%$ of printed price.
We know that $x\%$ of y = $\dfrac{x}{100}\times y$.
$\Rightarrow s=\dfrac{80}{100}\times p$.
$\Rightarrow s=0.8p$---(1).
According to the problem, we are given that the shop keeper earned a profit of $15\%$ on selling the book at a price of $0.8p$.
We know that $profit\%=\dfrac{selling\ price-\text{cost } price}{\operatorname{cost} price}\times 100$.
So, we get $15\%=\dfrac{0.8p-c}{c}\times 100$.
$\Rightarrow 0.15=\dfrac{0.8p}{c}-1$.
$\Rightarrow 1.15=\dfrac{0.8p}{c}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{0.8}{1.15}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{80}{115}$.
$\Rightarrow \dfrac{c}{p}=\dfrac{16}{23}$.
So, we have found the ratio of cost price and printed price of the book as $16:23$.
So, the correct answer is “Option (a)”.
Note: We can see that there are high chances of making mistakes while solving this problem. So, we need to solve each step properly in order to avoid the mistakes. We can also find the total amount profit gained by the shopkeeper after getting the ratio between cost price and the printed price, as we are taking all the values in terms of printed price. Similarly, we can also expect problems to find the selling price and price of the book.
Recently Updated Pages
The height of a solid metal cylinder is 20cm Its r-class-10-maths-ICSE

If a train crossed a pole at a speed of 60kmhr in 30 class 10 physics CBSE

Name the Writs that the High Courts are empowered to class 10 social science CBSE

A tower is 5sqrt 3 meter high Find the angle of el-class-10-maths-CBSE

Immediate cause of variations of A Mutations B Environmental class 10 biology CBSE

A rectangular container whose base is a square of side class 10 maths CBSE

Trending doubts
Who composed the song Vande Mataram A RabindraNath class 10 social science CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

The revolutionary who died after 63 days of the hunger class 10 social science CBSE

The slogan of Bande Mataram was first adopted during class 10 social science CBSE

Why is Sardar Vallabhbhai Patel called the Iron man class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

