Question

A farmer sold a cow and an ox for Rs. 800 and got a profit of 20\(\%\) on the cow and 25\(\%\) on the ox. If he sells the cow and the ox for Rs. 820 and gets a profit of 25\(\%\) on the cow and 20\(\%\) on the ox, the individual cost price of the cow and the ox is

• A. Rs. 515.60, Rs. 115.60 (Approx.)
• B. Rs. 531.50, Rs. 135.50 (Approx.)
• C. Rs. 530.60, Rs. 130.60 (Approx.)
• D. Cannot be determined

Answer 1

The Correct Option is C

Let the C.P. of the cow be Rs. x and that of the ox be Rs. y
Then,
= 120\(\%\) of x + 125\(\%\) of y = 800
⇒ \(\frac{6x}{5}+\frac{5y}{4}=800\)
⇒ 24x + 25y = 16000 .......(i)
And
125\(\%\) of x + 120\(\%\) of y = 820
⇒ \(\frac{5x}{4}+\frac{6y}{5}=820\)
⇒ 25x + 24y = 16400 ......(ii)
Adding (i) and (ii), we get :
49x + 49y = 32400
⇒ \(x+y=\frac{32400}{49}\)......(iii)
Subtracting (i) from (ii), we get :
x - y = 400 ........(iv)
Adding (iii) and (iv), we get :
\(2x=\frac{32400}{49}+400=\frac{52000}{49}\) 
⇒ \(x=\frac{26000}{49}\approx530.60\)
Putting \(x=\frac{26000}{49}\) in (iii),
we get:
\(y=\frac{32400}{49}-\frac{26000}{49}\)
\(=\frac{6400}{49}\approx130.60\)
The correct option is (C): Rs. 530.60, Rs. 130.60 (Approx.)