Linear Equation 28

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A farmer sold a calf and a cow for $ 760, thereby making a profit of 25 % on the calf and 10 % on the cow.
By selling them for $ 767.50, he would have realized a profit of 10 % on the calf and 25 % on the cow.
Find the cost price of each.

Solution:

Let the C.P. of the calf = $ x and the C.P. of the cow = $ y

In the first case :

S.P. of the calf = $ x + 25 % of $ x = $ (x + 25 x / 100) = $ 5 x / 4

S.P. of the cow = $ y + 10 % of $ y = $ (y + 10 y / 100) = $ 11 y / 10

Therefore, 5 x / 4 + 11 y / 10 = 760

=> 25 x + 22 y = 15200 ---------------------------------------------- (i)

In second case :

S.P. of the calf = $ x + 10 % of $ x = $ 11 x / 10

S.P. of the cow = $ y + 25 % of $ y = $ 5 y / 4

Therefore, 11 x / 10 + 5 y / 4 = 767.50

=> 22 x + 25 y = 15350 --------------------------------------------- (ii)

On solving equations (i) and (ii), we get

Therefore, C.P. of the calf = $ 300 and C.P. of the cow = $ 350

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