Question

A man has some hens and cows. If the number of heads be 48 and number of feet equals
140, the number of hens will be: (a) 22 (6) 23 (c) 24 (d) 26​

Answer 1

Answer

Option d) 26

$\rule{100}2$

Explanation

Let the number of hens be x and number of cows be y.

Given that number of heads are 48. (Here, 48 is the number of heads of hens and cows).

So, we can write it like. Sum of number of hens and cows is 48.

$\implies\:\sf{x\:+\:y\:=\:48}$

$\implies\:\sf{x\:=\:48\:-\:y}$ ---- [1]

Also, given that number of feet equals to 140.

We know that, a hen has two feet and a cow has four feet.

Sum of hen feet and cow feet is 140.

$\implies\:\sf{2x\:+\:4y\:=\:140}$

Take 2 common from both side

$\implies\:\sf{2(x\:+\:2y)\:=\:2(70)}$

$\implies\:\sf{x\:+\:2y\:=\:70}$

Substitute value of x = 48 - y in above equation

$\implies\:\sf{48\:-\:y\:+\:2y\:=\:70}$

$\implies\:\sf{y\:=\:70\:-\:48}$

$\implies\:\sf{y\:=\:22}$

Substitute value of y = 22 in equation (1)

$\implies\:\sf{x\:=\:48\:-\:22}$

$\implies\:\sf{x\:=\:26}$

•°• Number of hens will be 26 and cows will be 22.