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?

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.

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.