Question

A man sold two cycles for $Rs3000$ each, gaining $20\%$ on the and losing $20\%$ on the other. Find his gain or loss percentage on the whole transaction?

Answer 1

Given that,

$S.P$ of $1st$ cycle$=S.P$ of $2nd$ cycle$=Rs.3000$

Now on $1st$ cycle he had a profit of $20$%

$\therefore$ $C.P=\frac{S.P}{\left(1-\frac{gain\%}{100}\right)}$

$\begin{array}{c}=\frac{3000}{\left(1+\frac{20}{100}\right)}\\ =\frac{3000\times 100}{120}\\ =Rs.2500\end{array}$

$\therefore$ $CP$ of $1st$ cycle $=Rs.2500$

Again, on $2nd$ cycle he had a loss of $20$%

$C.P=\frac{S.P}{\left(1-\frac{loss\%}{100}\right)}$

$\begin{array}{c}=\frac{3000}{\left(1-\frac{20}{100}\right)}\\ =\frac{3000\times 100}{80}\\ =Rs.3750\end{array}$

$\therefore$ $CP$ of $2nd$ cycle $=Rs.3750$

Total $Cp$ of cycles $=2500+3750=Rs.6250$

Total $SP$ of cycles $+3000+3000=Rs.6000$

Loss=CP-SP

$=6250-6000=Rs.250$

$Loss\%=\frac{250\times 100}{6250}$

$=4$%

Then,

We get $4$%