Question & Answer
QUESTION

Juhi sells a washing machine for Rs. 13, 500. She loses 20% in the bargain. What was the price at which she bought it?

ANSWER Verified Verified
Hint: Assume the cost price to be x and then use the condition that 20% of cost price when reduced from the cost price i.e. ‘x’ you will get the selling price. By simplifying this equation you will get your final answer.

Complete step-by-step answer:
As Juhi sold the washing machine at Rs. 13, 500 therefore the selling price will become,
SP = Rs. 13,500 …………………………………………………… (1)
We will assume the cost price of the washing machine as ‘x’, therefore
CP = x ………………………………………………………………………… (2)
As per the given condition, Juhi loses 20% cost while selling the washing machine i.e. when 20% of the cost price is reduced from the cost price; we will get the value of selling price. Therefore 20% of the cost price can be given as,
20% of the cost price = 20% (CP)
If we put the value of equation (2) in the above equation we will get,
20% of the cost price = 20%(x)
Therefore, 20% of the cost price = $\dfrac{20}{100}x$ ………………………………………………………… (3)
Now, as per the condition we have mentioned earlier, if we reduce 20% of CP from CP it will give us the SP therefore we can write,
CP – 20% of CP = SP
If we put the values of equation (1), equation (2) and equation (3) in the above equation we will get,
 $x-\dfrac{20}{100}x=13500$
Taking ‘x’ common from the above equation will give,
$\therefore x\left( 1-\dfrac{20}{100} \right)=13500$
If we subtract the term $-\dfrac{20}{100}$ from ‘1’ in the above equation we will get,
$\therefore x\left( \dfrac{100-20}{100} \right)=13500$
By simplifying the above equation we will get,
$\therefore x\left( \dfrac{80}{100} \right)=13500$
Further simplification in the above equation will give,
$\therefore x\left( \dfrac{8}{10} \right)=13500$
By shifting $\dfrac{8}{10}$ on the right hand side of the equation will give,
$\dfrac{20}{100}CP$
$\therefore x=\dfrac{135000}{8}$
Therefore, x = Rs. 16875
Therefore the value of the cost price of the washing machine is equal to Rs. 16875.

Note: During exam there is chance of silly mistake that you can take only $\dfrac{20}{100}$ in place of $\dfrac{20}{100}CP$ or sometimes you add this value in CP as you are in hurry, but do remember that it will lead you to the wrong answer.