Question

A farmer bought a cow and a calf together for Rs. 14000. After some time, he sold the cow at a profit of 20% and the calf at a profit of 13%. On the whole he got a profit of 17%. Find the cost price of the cow and the calf.

• A. Rs. 8000, Rs. 6000
• B. Rs. 6000, Rs. 6000
• C. Rs. 8000, Rs. 8000
• D. Rs. 9000, Rs. 5000

Answer 1

The correct option is A Rs. 8000, Rs. 6000

Let x be the cost price of cow and $y$ be the cost price of calf.
$\therefore x+y=14000$ .........(i)
profit% on cow = 20%
$\therefore$ profit =$\frac{20}{100}x$
selling price of cow = cost price + profit
=$x+\frac{20}{100}x$
profit% on calf = 13%
$\therefore$ profit =$\frac{13}{100}y$
selling price of cow = cost price + profit
=$y+\frac{13}{100}y$
Farmer got profit on whole = 17%
$\therefore$ profit =$\frac{17}{100}\times 14000$
selling price of cow and calf = cost price of cow and calf + profit
$x+\frac{20}{100}x+y+\frac{13}{100}y=14000+\frac{17}{100}\times 14000$
$\therefore 1.2x+1.13y=16380$ .......(ii)
Multiplying equation (i) by $1.2$. we get,
$1.2x+1.2y=16800$ ....(iii)
On subtracting (iii) from (ii). we get,
$1.13y-1.2y=16380-16800$
$\therefore 0.07y=420$
$\therefore y=6000$
On substituting $y=6000$ in (i). we get,
$x+6000=140000$
$\therefore x=8000$
$\therefore$ cost of cow = Rs. 8000
and cost of calf = Rs. 6000