Question

03 A shopkeeper bought two television sets for Rs. 50,000 each. He sold one of them at a loss
of 20% and other at a gain of 25%. Find the profit or loss on the whole transaction.
(3)​

Answer 1

GiveN:-

A shopkeeper bought two television sets for Rs. 50,000 each. He sold one of them at a loss of 20% and other at a gain of 25%.

To FinD:-

Find the profit or loss on the whole transaction.

SolutioN:-

• We are given the CP of two television sets. So we have to find out the SP of the two television sets.
• Then we will be adding the CP of two television sets. Same for SP.
• Now by comparing the total SP and total CP we can find the profit or loss.

1)) SP of 1st television :

• CP = Rs.50,000
• Loss% = 20%
• We have to find the SP.

We know that,

$\small{\green{\underline{\boxed{\bf{SP=\left(1-\dfrac{Loss\%}{100}\right)\times\:CP}}}}}$

where,

• CP = Rs.50,000
• Loss% = 20%
• SP = ?

Putting the values,

:$\small\implies{\sf{SP=\left(1-\dfrac{20\%}{100}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(1-\dfrac{\cancel{20}}{\cancel{100}}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(1-\dfrac{1}{5}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(\dfrac{5-1}{5}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(\dfrac{4}{5}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\dfrac{4}{5}\times\:50000}}$

:$\small\implies{\sf{SP=\dfrac{4}{\cancel{5}}\times\:\cancel{50000}}}$

:$\small\implies{\sf{SP=4\times10000}}$

$\large\therefore\boxed{\bf{SP=Rs.40,000}}$

2)) SP of 2nd television :

• CP = Rs.50,000
• Gain% = 25%
• We have to find the SP.

We know that,

$\small{\green{\underline{\boxed{\bf{SP=\left(1+\dfrac{Gain\%}{100}\right)\times\:CP}}}}}$

where,

• CP = Rs.50,000
• Gain% = 25%
• SP = ?

Putting the values,

:$\small\implies{\sf{SP=\left(1+\dfrac{25\%}{100}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(1+\dfrac{\cancel{25}}{\cancel{100}}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(1+\dfrac{1}{4}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(\dfrac{4+1}{4}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\left(\dfrac{5}{4}\right)\times\:50000}}$

:$\small\implies{\sf{SP=\dfrac{5}{4}\times\:50000}}$

:$\small\implies{\sf{SP=\dfrac{5}{\cancel{4}}\times\cancel{50000}}}$

:$\small\implies{\sf{SP=5\times12500}}$

$\large\therefore\boxed{\bf{SP=Rs.62,500.}}$

• Now we got the SP of both the television.
• So we have to find the total CP and total SP.

Total CP :

:$\small\implies{\sf{Total\:CP=Rs.(50,000+50,000)}}$

$\large\therefore\boxed{\bf{Total\:CP=Rs.1,00,000.}}$

Total SP :

:$\small\implies{\sf{Total\:SP=Rs.(40,000+62,500)}}$

$\large\therefore\boxed{\bf{Total\:SP=Rs.1,02,500.}}$

• Here we can see that the SP > CP = 102500 > 100000
• As said if SP is greater than CP then it is a profit.

Profit :

We know that,

$\small{\green{\underline{\boxed{\bf{Profit=SP-CP}}}}}$

where,

• SP = Rs.1,02,500
• CP = Rs.1,00,000

Putting the values,

:$\small\implies{\sf{Profit=Rs.(1,02,500-1,00,000)}}$

$\large\therefore\boxed{\bf{Profit=Rs.2,500}}$

The profit on whole transaction is Rs.2,500.