Question

A farmer sold a calf and a cow for Rs 760 ,thereby , making a profit of 25% on the calf and 10% on the cow by selling them for rupees 767.50 he would have realised a profit of 10 % on calf and 25% on cow . find the cost of each

Answer 1

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Answer 2

The cost price of the cow is Rs 350 and cost price of the calf is Rs 300

Let the C.P. of cow be Rs 'x' and the C.P. of the calf be Rs 'y'.

S.P. of calf after 25% profit = (100+profit)% of CP

= (100+25)% of y

= 1.25y

S.P. of cow after 10% profit

= 110% of x

= 1.1x

Total S.P. = (1.25y + 1.1x)

Given that the selling price is 760.

So, (1.25y + 1.1x) = 760                                                          

⇒1.1x = 760 - 1.25y

⇒x = 760/1.1 - 1.25y/1.1                                                                ...(1)

S.P. of cow after 25% profit = (100+profit)% of CP

= (100+25)% of x

= 1.25x

S.P. of calf after 10% profit

= 110% of y

= 1.1y

Total S.P. = (1.25x + 1.1y)

Given that the selling price is 767.50.

So, (1.25x + 1.1y) = 767.50                                                          ...(2)

Putting the value of 'x' from (1) in (2), we get:

1.25(760/1.1 - 1.25y/1.1) + 1.1y = 767.50

⇒ 863.64 - 1.42y + 1.1y = 767.50

⇒ 1.42y - 1.1y = 863.64 - 767.50

⇒ 0.32y = 96.14

⇒ y = 96.14/0.32 ≈ 300

Putting the value of y in eq.(2), we get:

1.25x + 1.1(300) = 767.50

⇒ 1.25x = 767.50 - 330 = 437.50

⇒  x = 437.50/1.25 = 350

x = Rs 350

y = Rs 300