Question

A trader sells two cycles at Rs $1188$ each and gains $30\%$ on the first and loses $30\%$ on the second. What is the profit or loss on the whole transaction?

• A. $1\%$ loss
• B. no profit, no loss
• C. $9\%$ loss
• D. $1\%$ gain

Answer 1

Answer: (C)

$9\%$ loss

Selling Price of two cycles $=1188$ Rs each

Total selling price $=1188\times 2=2376Rs$

Trader gains $30\%$ on first cycle.

Let's assume CP of cycle $=x$ Rs

Then, $SP=CP+CP\times \frac{GainPercentage}{100}$

$\Rightarrow 1188=x+x\times \frac{30}{100}$

$\Rightarrow 1188=\frac{13x}{10}$

$\therefore x=\frac{1188\times 10}{13}=\frac{11880}{13}Rs$

Also, trader loses $30\%$ on another cycle.

Let's assume CP of this cycle $=y$ Rs

Then, $SP=CP-CP\times \frac{LossPercentage}{100}$

$\Rightarrow 1188=y-y\times \frac{30}{100}$

$\Rightarrow 1188=\frac{7y}{10}$

$\therefore y=\frac{1188\times 10}{7}=\frac{11880}{7}Rs$

Hence, Total CP = $x+y=\frac{11880}{13}+\frac{11880}{7}=\frac{83160+154440}{91}=\frac{237600}{91}Rs=2610.99Rs=2611Rs$

Here CP > SP.

So, $loss=CP-SP=2611-2376=235Rs$

$\therefore LossPercentage=\frac{loss\times 100}{CP}=\frac{235\times 100}{2611}=9\%$