Question

Raj counted 80 heads and 180 legs among the sheep and ducks in his farm. How many ducks does he have? A.70 b. 65 c. 72 d. 75​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Raj counted 80 heads and 180 legs among the sheep and ducks in his farm.

Let us assume that

➢ Number of ducks = x

and

➢ Number of sheeps = y

According to first condition,

Total number of heads = 80

$\rm :\longmapsto\:x + y = 80 - - - (1)$

According to second condition,

➢ Total number of legs = 180

➢ Now, duck has 2 legs and sheep has 4 legs

$\rm :\longmapsto\:2x + 4y = 180$

$\rm :\longmapsto\:x + 2y = 90 - - - - (2)$

Now, Subtracting equation (2) from equation (2), we get

$\rm :\longmapsto\:x + 2y - (x + y) = 90 - 80$

$\rm :\longmapsto\:x + 2y - x - y = 10$

$\bf\implies \:y = 10$

On substituting value of y = 10, in equation (1), we get

$\rm :\longmapsto\:x + 10 = 80$

$\bf\implies \:x = 70$

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: So-\begin{cases} &\sf{number \: of \: ducks = 70} \\ &\sf{number \: of \: sheeps = 10} \end{cases}\end{gathered}\end{gathered}$

Hence,

• Option A. is correct