Question

A trader sells a machine for 27500Rs. If he sells it at 10%lower value then he has a 10% profit. what is the actual purchase price of the machine?

Answer 1

We are provided the following information,

Selling Price ( SP ) = ₹ 27500
Profit percentage when SP is 10 % less = 10 %

$\large\underline\bold{Solution:\longrightarrow}$

Actual SP = ₹ 27500

Imaginary SP = Actual SP - 10% of Actual SP
Imaginary SP = ₹ 27500 - 10/100 of ₹ 27500
Imaginary SP = ₹ 27500 - ₹ 2750
Imaginary SP = ₹ 24750

When machine is sold at imaginary SP then 10 % profit is enjoyed.

Let the Cost Price be ₹ x

Now we know that,

Profit = SP - CP
Profit = ₹ ( 24750 - x )

Profit percentage = ( Profit / CP ) * 100
10 = $\bold{\frac{24750 - x}{x} \times 100 \\}$
10 = ( 24750 - x ) / x * 100
10x = 100 ( 24750 - x )
x = 10 ( 24750 - x )
x = 247500 - 10x
11 x = 247500
x = ₹ 22500

Hence,

Cost price/Purchasing price of machine = ₹ 22500

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