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A man purchases two clocks A and B at a total cost of Rs 650. He sells A at 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

Easy

Solution

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Correct option is C)

Let the cost price (C.P) of A be Rs x

and that of B be Rs y 3

Total cost =Rs650 - [Given]

∴x+y=650

For A

Profit =20%

Profit %=

C.P

Profit

×100

∴20=

C.PofA

sellingpriceof(S.P)−C.PofA

×100

∴

5

1

=

x

S.P−x

∴S.P. of A=

5

6x

For B

Loss =25%

Loss%

C.P

Loss

×100

25=

C.PofB

C.PofB−sellingprice(S.P)ofB

×100

4

1

=

y

y−S.P

4

y

=y−S.P. of B

∴ SP of B =

4

3y

But, according to the given concoction

S.P of A=S.P of B

5

6x

=

4

3y

5

6x

−

4

3y

=0

8x−5y=0...(2)

Multiplying equation (1) by 5

∴5x+5y=3250...(3)

Adding equations (2) and (3)

∴8x+5y+5x+5y=0+3250

13x=3250

x=Rs250

Substituting the above value in equation (1)

∴250+y=650

∴y=Rs400

∴ Cost price of A=Rs250

∴ Cost price of B=Rs400