Question

In a group there are goats and hens . The total no. of legs is 124 and total no. of heads is 40 . Find the no. of goats and hens.

Answer 1

Hi There!

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Let the total No. Of Goats be $x$

And Total no. of Hens be $y$

Total given legs = 124

It means, Legs of Goats as well as Hens = 124

Goats were $x$ But,

∵ A Goat has got 4 legs and A Hens has got 2,

∴ 4$x$ + 2$y$ = 124 .....(i)

⇒ 2$x$+ $y$ = 62 ......(ii) {Dividing by 2 both the sides}

Total Given Heads, = 40

∵ Goat and Hen, Both have only 1 head,

∴ 1$x$ + 1$y$ = 40 ....(iii)

From Equation (ii) and (iii),

We Have,

2$x$+ $y$ = 62

1$x$ + 1$y$ = 40

On Subtracting (iii) from (ii),

2$x$ - 1$x$ + $y$ - $y$ = 62- 40

∴ +y and -y gets cancelled, And

∴ $x$ = 62-40

∴ $x$ = 22

But, 1$x$ + 1$y$ = 40

∵ $x$ = 22

On Putting value,

1 × 22 + 1$y$ = 40

22 + $y$ = 40

$y$= 40-22

$y$ = 18

$\boxed{ No. Of Goats = 22 And No. Of Hens = 18}$

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Thanks!!

Hope This Helps!!!

$\boxed{@Ben4Brainly}$

Answer 2

Hii There!!!
See the above attachment......
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