Subject: General Aptitude · Chapter: Profit and Loss · Exam: 2005 · Marks: · Difficulty:
A farmer sold a cow and an ox for ₹ 800 and got a profit of 20\% on the cow and 25\% on the ox. If he sells the cow and the ox for ₹ 820 he 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)₹ 530.60, ₹ 130.60 (approx)
(b)₹ 515.60, ₹ 115.60 (approx)
(c)₹ 531.50, ₹ 135.50 (approx)
(d)Cannot be determined
Answer
Answer (as printed): A
Explanation
Let the C.P. of the cow be ₹ $x$ and that of the ox be ₹ $y$. Then, $120 \%$ of $x+125 \%$ of $y=800 \Rightarrow \frac{6 x}{5}+\frac{5 y}{4}=800$ $$\Rightarrow 24 x+25 y=16000$$ And, $125 \%$ of $x+120 \%$ of $y=820 \Rightarrow \frac{5 x}{4}+\frac{6 y}{5}=820$ $$\Rightarrow 25 x+24 y=16400$$ Adding (i) and (ii), we get : $49 x+49 y=32400$ $$\Rightarrow x+y=\frac{32400}{49}$$ Subtracting (i) from (ii), we get : $x-y=400$ Adding (iii) and (iv), we get : $$2 x=\frac{32400}{49}+400=\frac{52000}{49} \Rightarrow x=\frac{26000}{49} \approx 530.60 .$$ Putting $x=\frac{26000}{49}$ in (iii), we get: $$y=\frac{32400}{49}-\frac{26000}{49}=\frac{6400}{49} \approx 130.60 .$$
Explanation as extracted from the printed page; notation may be imperfect.