Question

A man purchase 5horses and 10 cows for Rs 10,000. He sells the horses at 15% profit and the cows at 10%loss.Thus he gets Rs 375 as profit. Find the cost of 1horse and 1cow.
without allegation.

Answer 1

Hi ,

Let us assume that ,

Cost price of each horse = Rs x

Cost price of each cow = Rs y

Gain of selling the horse ( g ) = 15%

Loss if selling the cow ( L ) = 10%

S.p of horse = x ( 100 + g )/100

= x ( 100 + 15 )/100

= 115x/ 100

S.p of 5 horses = 5 × 115x/100

= 23x/4 ---( 1 )

S.p of each cow = y ( 100 - L )/100

= y × ( 100 - 10 )/100

= 90y/100

S.p of 10 cows = 10 × 90y/100

= 9y ---( 2 )

Profit of selling horses = 23x/4 - 5x

= ( 23x - 20x )/4

= 3x/4 --- ( 3 )

Loss of selling cows = 10y - 9y

= y--( 5 )

According to the problem given ,

Man gets Rs 375 profit

( 4 ) - ( 5 ) = 375

3x/4 - y = 375

( 3x - 4y ) = 375 × 4

3x - 4y = 1500 ---( 6 )

Cost price of 5 horses and 10 cow's

is Rs 10000

5x + 10y = 10000

x + 2y = 2000

x = 2000 - 2y ----- ( 7 )

Substitute ( 7 ) in equation ( 6 ) ,we

get

3( 2000 - 2y ) - 4y = 1500

6000 - 6y - 4y = 1500

- 10y = 1500 - 6000

- 10y = - 4500

y = Rs 450

Now ,

Substitute y = 450 in equation ( 7 ) ,

we get

x = 2000 - 2 × 450

x = 2000 - 900

x = 1100

Therefore ,

Cost of each horse = x = Rs 1100

Cost of each cow = y = Rs450

I hope this helps you.

: )