Question

A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs. 3150. Find at what price he must sell the first grade bicycles so that if he sells the second grade bicycles at three quarters of the price, he may make a profit of 40% on his out lay?
a. Rs. 200
b. Rs. 240
c. Rs. 180
d. Rs. 210

Answer 1

Hint: We will assume the selling price of a first grade bicycle as Rs. x and the selling price of the second grade bicycle as Rs. $ \dfrac{3x}{4} $ . And we will get the selling price of 30 bicycles as Rs. $ \left( \dfrac{140}{100}\times 3150 \right) $ . So, we get an equation, $ 8x+\dfrac{22\left( 3x \right)}{4}=3150\times 1.4 $ . We will solve the equation to get the selling price of the first grade bicycles.

Complete step-by-step answer:
It is given in the question that a cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs. 3150. And we have been asked to find at what price he must sell the first grade bicycles so that if he sells the second grade bicycles at three quarters of the price, he may make a profit of 40% on his outlay.
Let us assume that the selling price of a first grade bicycle is Rs. x. And according to the condition given in the question, that the selling price of a second grade bicycle is three quarters of the selling price of first grade bicycles. So, we get the selling price of one second grade bicycle as $ Rs.\left( \dfrac{3x}{4} \right) $ .
Now, we are given that the cost of 30 bicycles is Rs. 3150 and the profit percentage is 40%.
We know that the selling price can be found out using the formula, $ SP=\left( \dfrac{100+profit\text{ }percentage}{100}\times CP \right) $ .
So, we can find the SP or the selling price of 30 bicycles using the above formula, where the CP or cost price is Rs. 3150 and the profit percentage is 40%. Therefore on substituting these values in the formula, we will get,
 $ \begin{align}
  & SP=\left( \dfrac{100+40}{100}\times 3150 \right) \\
 & =\dfrac{140}{100}\times 3150 \\
 & =1.4\times 3150 \\
 & =Rs.4410 \\
\end{align} $
Now, in the question we are given that there are 8 first grade bicycles and the total number of bicycles is 30. So, the remaining number will be the second grade bicycles. So, we get the number of second grade bicycles as (30 - 8) = 22. So, we can write,
Selling price of 8 first grade bicycles + selling price of 22 second grade bicycles = selling price of 30 bicycles
 $ \begin{align}
  & 8x+22\times \dfrac{3x}{4}=4410 \\
 & 8x+\dfrac{66x}{4}=4410 \\
 & \dfrac{32x+66x}{4}=4410 \\
 & \dfrac{98x}{4}=4410 \\
\end{align} $
On cross multiplying, we get,
 $ \begin{align}
  & 98x=4\times 4410 \\
 & 98x=17640 \\
 & x=\dfrac{17640}{98} \\
 & x=180 \\
\end{align} $
Thus, the selling price of a first grade bicycle will be Rs. 180.
Hence, option (c) is the correct answer.

Note: The possible mistakes that the students can make in this question is that they may take the selling price of 30 bicycles as $ \dfrac{40}{100}\times 3150 $ which is equal to 1260, hence they will get the final equation as, $ 8x+22\times \dfrac{3x}{4}=1260 $ , which is not correct so the students will get the wrong answer. But actually, the selling price of 30 bicycles is $ SP=\left( \dfrac{100+40}{100}\times 3150 \right) $ which we get from the formula, $ SP=\left( \dfrac{100+profit\text{ }percentage}{100}\times CP \right) $ .