Question

A man purchases 2 horses and 3 cows for rs 72000. he sells the horses at 15% profit and cows at 5% loss. if in this way he gets a total profit of rs 8000 then what is the total cost of one horse and one cow?

Answer 1

Let the cost of one horse be 'x'
Then the cost of 2 horses are 2x

Let the C.P of one cow be 'y'
Then the C.P of 3 cows are 3y

Given that
2x + 3y = 72000 ------------------ (1)

15 percent of 2 horses = 30x/100
5 percent of 3 cows = 15y/100

S.P of 2 horses = C.P + Profit = 2x + 30x/100 = (200x+30x)/100 = 230x/100

S.P of 3 cows = C.P - Loss = 3y - 15y/100 = (300y-15y)/100 = 285y/100

S.P of 2 horses and 3 cows = 230x/100 + 285y/100 = (230x+285y)/100

Total profit = 8000 rs

=> S.P - C.P = 8000 rs

=> (230x + 285y)/100 - 72000 = 8000

=> 230x + 285y = 8000000 --------------- (2)

Solving (1) and (2) we will get x=22500 and y=9000

Total cost of one cow and one horse = 22500 + 9000 = 31500 rs

The answer is 31500 rs

Hope it helps

Answer 2

Solution :-

Let the cost price of eaxh horse be Rs. h and the cost price of one cow be Rs. c

Then, according to the question.

⇒ 2h + 3c = 72000 ................(1)


He sells the horses at a profit of 15 % and sells the cows at a loss of 5 % 

⇒ (2h*15)/100 + (3c*5)/100 = 8000

⇒ 3h/10 + 3c/20 = 8000

⇒ (6h + 3c)/20 = 8000 

⇒ 6h + 3c = 160000 ............(2)

Now, subtracting equation (1) from (2), we get

⇒ 6h + 3c = 160000
    2h + 3c =  72000
  -      -         -   
________________
   4h         = 88000
__________________

 4h = 88000

h = 22000

So, cost of each horse is Rs. 22000

Putting the value of h = 22000 in (1)

2h + 3c = 72000

2*22000 + 3c = 72000

44000 + 3c = 72000

3c = 72000 - 44000

c = 28000/3

c = 9333 

So, the cost of each cow is Rs. 9333 (Approximately)

Answer.