Question

A shopkeeper sold two fans for $Rs.1140$ each. On one he gains $14$% while on the other he loses $5$%. Calculate his gain or loss percent in the whole transaction.

Answer 1

Let CP be the cost price of the fan each.

Let $S{P}_1$ be the selling price of the $1^{st}$ fan.

Let $S{P}_2$ be the selling price of the $2^{nd}$ fan.

Let SP be the selling price of both the fans together.

i.e., $SP=S{P}_1+S{P}_2$

Profit of the $1^{st}$ fan(in percentage)$=14$

$\Rightarrow \frac{S{P}_1-CP}{CP}\times 100=14$

$\Rightarrow S{P}_1-CP=\frac{14}{100}CP$

$\Rightarrow S{P}_1=\frac{14}{100}CP+CP$

$\Rightarrow S{P}_1=\frac{114}{100}CP$ ……….$\left(1\right)$

Loss of the $2^{nd}$ fan(in percentage)$=5$

$\Rightarrow \frac{CP-S{P}_2}{CP}\times 100=5$

$\Rightarrow CP-S{P}_2=\frac{5}{100}CP$

$\Rightarrow S{P}_2=CP-\frac{5}{100}CP$

$\Rightarrow S{P}_2=\frac{95}{100}CP$ ………$\left(2\right)$

As per question, $SP=1140$

$S{P}_1+S{P}_2=1140$

$\frac{1140}{100}CP+\frac{95}{100}CP=1140$

$\Rightarrow \frac{209}{100}CP=1140$

$\Rightarrow CP=\frac{1140\times 100}{209}$

$\Rightarrow CP=545.45$(approx.)

$\therefore$ Cost price of both the fans together$=2\times 545.45$

$=1090.90$ (approx.)

Gain in the whole transaction(in percentage)$=\frac{1140-1090.90}{1090.90}\times 100$

$=4.5\%$(approx.).