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

Answer: (C)

Rs. $180$

Let the S.P.of one $A$ grade cycle $=$ Rs. $n$
Then, the S.P. of one $B$ grade cycle $=$ Rs. $\frac{3n}{4}$

C.P. of $30$ cycles $=$ Rs. $3150$, profit $=40\%$.
$\therefore$ S.P. of $30$ cycles $=\frac{140}{100}\times 3150=$ Rs. $3150\times 1.4$

According to the question, we have
$8n+22\times \frac{3n}{4}=3150\times 1.4$
$\Rightarrow 32n+66n=17640$

$\Rightarrow 98n=17640$

$\Rightarrow n=180$
Therefore, he should sell the first grade bicycle at Rs. $180$ each.