Question

Malik sells two tables for $Rs.3000$ each. He gains $20\%$ on one table and on the other he loses $20\%$. Find his gain or loss percent on the whole transaction.

Answer 1

Selling Price of each table $=Rs.3000$

Case 1:

Gain on Table1 $=20\%$,

$\Rightarrow SP=CP+20\%$ of $CP$

$\Rightarrow Rs.3000=CP+\frac{20}{100}CP$

$\Rightarrow Rs.3000=\frac{120}{100}\times CP$

$\Rightarrow Rs.3000\times \frac{100}{120}=CP$

$\Rightarrow Rs.250\times 100=CP$

$\Rightarrow CP=Rs.2500$ ---(1)

Case 2:

Loss on table 2 $=20\%$

$\Rightarrow SP=CP-20\%$ of $CP$

$\Rightarrow Rs.3000=CP-\frac{20}{100}CP$

$\Rightarrow Rs.3000=\frac{80}{100}\times CP$

$\Rightarrow Rs.3000\times \frac{100}{80}=CP$

$\Rightarrow Rs.37.5\times 100=CP$

$\Rightarrow CP=Rs.3750$ ---(2)

From (1) and (2),

Total $CP=Rs.2500+Rs.3750=Rs.6250$

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

Since, $CP>SP$

So, Malik incurs Loss.

Loss $=SP-CP=Rs.6520-Rs.6000=Rs.250$

Loss percentage $=\frac{\text{Loss}}{\text{CP}}\times 100$

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

$=\frac{100}{25}$

$=4$

Therefore, Malik get $4\%$ loss on the whole transaction.