Question

After a 20% hike, the cost of a refrigerator is ₹15300. What was the original price of this
refrigerator?​

Answer 1

Answer :-

• The original price of the refrigerator was Rs 12750.

Given :-

• After a 20% hike, the cost of a refrigerator is Rs 15300.

To find :-

• The original price of this refrigerator.

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Step-by-step explanation :-

Let the original price of the refrigerator be Rs x.

According to the question,

$\sf x + 20\% \: of \: x =Rs \: 15300$

Converting 20% into fraction,

$\sf x + \dfrac{20}{100} \: of \: x = Rs \: 15300$

Cutting off the zeroes,

$\sf x + \dfrac{2}{10} \: of \: x = Rs \: 15300$

Reducing 2 and 10 by 2,

$\sf x + \dfrac{1}{5} \: of \: x = Rs \: 15300$

Multiplying $\sf \dfrac{1}{5}$ by x,

$\sf x + \dfrac{x}{5} = Rs \: 15300$

Now, lets add them like fractions.

x can also be written as $\sf \dfrac{x}{5}$

$\sf \dfrac{x}{1} + \dfrac{x}{5} = Rs \: 15300$

LCM of 1 and 5 is 5, so lets take it as the denominator.

$\sf \dfrac{(x \times 5) + (x \times 1)}{5} = Rs \: 15300$

On simplifying,

$\sf \dfrac{5x + x}{5} = Rs \: 15300$

Adding x to 5x,

$\sf \dfrac{6x}{5} = Rs \: 15300$

Transposing 5 from LHS to RHS, changing its sign,

$\sf 6x = Rs \: 15300 \times 5$

Multiplying,

$\sf 6x = Rs \: 76500$

Transposing 6 from LHS to RHS, changing its sign,

$\sf x = \dfrac{Rs \: 76500}{6}$

Dividing Rs 76500 by 6,

$\sf x = Rs \: 12750.$

So, the value of x = Rs 12750.

Therefore, the original price of the refrigerator was Rs 12750.

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