Question

Q) A machine was sold at a profit of 10% . Had it been sold for Rs 400 less there would have been loss of 10 %. Find CP of machine.​

Answer 1

The answer is Rs 200.

Let’s say, Cost Price (C.P.) of the machine was x.

So with 10% profit, it was sold at 1.1x

Now, had it been sold at Rs 40 less, (1.1x - 40), it would have incurred a loss of 10%

So 1.1x - 40 = 0.9x

i.e. 1.1x - 0.9x = 40

i.e. x = 200

Hope this helps :)

Answer 2

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Let the cost price be “X”

& Profit be “0.1X”

So, Selling Price =X+0.1X=1.1X

Revised Selling price = (1.1X-40)

loss of 10%=( 0.9X-X)= -0.1X

Now as per the question stated:

Revised selling price -Cost price= loss of 10% i.e.,

[(1.1X-40)-X]= -0.1X

0.1X+0.1X=40

X=40/0.2=200

NOW YOU CAN CHECK THE EQUATION

BY PUTTING VALUE OF “X” WHICH GOES LIKE THIS:

[{(1.1 x 200)-40}-200]= (-0.1x200)

[{220-40}-200]=-20

[180-200]= -20

-20 =-20

implying that

LHS=RHS

THUS THE COST PRICE IS RS 200 & ORIGINAL SELLING PRICE IS 220.

BUT IF YOU SELL THE PRODUCT AT ITS

REVISED SELLING PRICE THAT IS RS 180

THEN YOU SUFFER THE LOSS OF RS 20

ONLY.