A shopkeeper bought a sunglass and sold it at a profit of 20% to a customer if the customer paid Rs 21,696 for it with 13% VAT, at what price did the shopkeeper buy it.

Answer: Rs 15,360

Solution:

For a sunglass,

Profit percentage (P%) = 20%

Selling Price with VAT (SP with VAT) = Rs 21,696

VAT percentage (VAT%) = 13%

To find: Cost Price (CP) = ?

We know,

$SP = \dfrac{SP with VAT}{100 + \frac{VAT%}{100}}$

$or, SP = \dfrac{21696}{100 + \frac{13}{100}}$

$or, SP = \dfrac{21696}{\frac{113}{100}}$

$or, SP = 21696 × \dfrac{100}{113}$

$\therefore SP = Rs 19200$

Now,

$CP = SP(1 - \frac{P%}{100})$

$or, CP = 19200 ( 1 - \frac{20}{100})$

$or, CP = 19200 ( \frac{80}{100})$

$\therefore CP = Rs 15360$

Hence, the shopkeeper bought the sunglasses at Rs 15360 and sold it.

#SciPiPupil