Question

A man buys two cycles for a total cost of $Rs.900$. By selling one cycle at a loss of $20\%$ and the other at a profit of $25\%$, he makes a profit of $Rs.90$ on the whole transaction. Find the cost price of each cycle.

• A. Rs. $200$; Rs. $700$
• B. Rs. $300$; Rs. $600$
• C. Rs. $400$; Rs. $500$
• D. Rs. $100$; Rs. $800$

Answer 1

The correct option is B Rs. $300$; Rs. $600$

Let cost prices of cycles be $Rs.x$ and $Rs.(900-x)$ respectively.

For the first cycle, he will lose $20\%$ i.e. $\frac{1}{5}$ of cost price, but for second cycle, he will gain $25\%$ i.e. $\frac{1}{4}$ of the cost price.

According to the question,

$\Rightarrow Profit-loss=90$

$\Rightarrow \frac{1}{4}of(900-x)-\frac{1}{5}ofx=90$

$\Rightarrow$ $\frac{900-x}{4}-\frac{x}{5}=90$

$\Rightarrow$ $5(900-x)-4x=1800$

$\Rightarrow$ $4500-5x-4x=1800$

$\Rightarrow$ $4500-9x=1800$

$\Rightarrow$ $9x=2700$

$\Rightarrow$ $x=300$

So, $900-x=900-300=600$

$\therefore$ The cost prices of the cycles are $Rs.300$ and $Rs.600$.