Question

Joe purchased 20 apples from a supermarket for 180 rupees at a discount of 10 percent. How much will a dozen apples cost him if he does not avail any discount?
(a) Rs. 108
(b) Rs. 120
(c) Rs. 132
(d) Rs. 144

Answer 1

Hint: From the cost of 20 apples given, find the cost of 1 apple using a unitary method. Find the cost of 1 apple if there is no discount. Now, multiply the cost of one apple with the number contained in 1 dozen, that is 12, to get the answer.

Complete step-by-step answer:

We have been given that the cost of 20 apples with a discount is Rs. 180. Therefore, using the unitary method, the cost of 1 apple with discount $=\dfrac{180}{20}=9$rupees. Assume that the original cost price of 1 apple is Rs. $x$. Now, the selling price of 1 apple is $90%$ of $x$, because $10%$ is a discount. Therefore, the selling price of 1 apple with discount is $\dfrac{90}{100}\times x=\dfrac{9x}{10}$ rupees.

$\begin{align}

  & \Rightarrow \dfrac{9x}{10}=9 \\

 & \Rightarrow x=\dfrac{90}{9} \\

 & \Rightarrow x=10 \\

\end{align}$

Therefore, the cost price of one apple without discount is Rs. 10. So, the cost of one dozen apples, that is 12 apples will be equal to the product of the number of apples with the cost of one apple. Therefore,

Cost of 12 apples

$\begin{align}

  & =12\times 10 \\

 & =120\text{ rupees} \\

\end{align}$

Hence, option (b) is the correct answer.

Note: We have used the basic unitary method to solve the question. One may notice that first we have calculated the amount of one apple with discount, then, the amount of one apple without discount is calculated. Finally, it is multiplied by 12 to get the answer. This is the basic approach used in the solution.