Question

A merchant buys $40$ bicycles and marks them at $25\%$ above the cost price. He allows a discount on the marked price at $10\%$ for cash sales and at $5\%$ for credit sales. If three fourth of the stock is sold for cash and the rest for credit and if the total profit is $Rs2025$, what is the cost price of one bicycle?

• A. $Rs350$
• B. $Rs720$
• C. $Rs360$
• D. $Rs460$

Answer 1

The correct option is C $Rs360$

There are $40$ bicycles.

Three fourth of they are sold in cash,

$40\times \frac{3}{4}=30$

Let the cost price of $1$ bicycle $=x.$

Then the total cost $=40x.$

Now the marked price of $1$ bicycle at $25\%$ profit will be,

$x(1+\frac{25}{100})=\frac{5x}{4}$

CASH SALE-

After a discount of $10\%,$ the $SP$ of $30$ bicycles,

$S{P}_1=\frac{5x}{4}(1-\frac{10}{100})\times 30$

$=\frac{135x}{4}$

CREDIT SALE-

After a discount of $5\%,$ the $SP$ of $10$ bicycles,

$S{P}_2=\frac{5x}{4}(1-\frac{5}{100})\times 10$

$=\frac{95x}{8}$

So, the total $SP$ will be,

$SP=S{P}_1+S{P}_2$

$=\frac{135x}{4}+\frac{95x}{8}$

$=\frac{365x}{8}$

$\text{Profit}=\frac{365x}{8}-40x$

$\Rightarrow 2025=\frac{45x}{8}$

$\Rightarrow x=Rs360$

Hence, option $C$ is correct.