Question

At a certain time in a zoo the number of heads and number of legs of human visitor and animal were counted and it was found that there were 78 heads and 216 legs . find the number of animals and human visitors in the zoo.​

Answer 1

$\sf\large\underline\purple{Let:-}$

$\sf{\implies The\: number\:of\:men=m}$

$\sf{\implies The\: number\:of\: animals=a}$

$\sf\large\underline\purple{Given:-}$

$\sf{\implies The\: number\:_{(heads)}=78}$

$\sf{\implies The\: number\:_{(legs)}=216}$

$\sf\large\underline\purple{To\: Find:-}$

$\sf{\implies The\: number\:_{(men\:and\: animals)}=?}$

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

• To calculate the number of men and animals at first we have to set up equation with the help of given clue in the question, as you know that a man has 2 legs and animal has 4 legs:-]

$\sf{\implies Man\:_{(head)}+Animal\:_{(head)}=78}$

$\tt{\implies m+a=78-----(i)}$

$\sf{\implies Men\:_{(legs)}+Animals\:_{(legs)}=78}$

$\tt{\implies 2m+4a=216----(ii)}$

• In eq (i) multiplying by 2 then subtract from eq (ii):-

$\tt{\implies 2m+2a=156}$

$\tt{\implies 2m+4a=216}$

• By solving we get, here:-

$\tt{\implies -2a=-60\implies a=30}$

• In eq (i) putting the value of a=30:-]

$\tt{\implies m+a=78}$

$\tt{\implies m+30=78}$

$\tt{\implies m=78-30\implies m=48}$

$\sf\large{Hence,}$

$\sf{\implies The\: number\:of\:men=48}$

$\sf{\implies The\: number\:of\: animals=30}$

Answer 2

$\sf{\pink{\underline{\underline{\purple{GIVEN:-}}}}}$

• At a certain time in a zoo the number of heads and number of legs of human visitor and animal were counted and it was found that there were 78 heads and 216 legs .

$\sf{\pink{\underline{\underline{\purple{TO\: FIND:-}}}}}$

• The number of animals and human visitors in the zoo .

$\sf{\pink{\underline{\underline{\purple{SOLUTION:-}}}}}$

Let,

• Number of animals = X

• Number of human visitors = Y

✍️ We have know that,

• Each animal have one head .

• And each human visitor has also one head .

✯ So According to the question,

$\orange\star\:\rm{\gray{\underline{\underline{\red{X\:+\:Y\:=\:78\:}}}}}$ ----(1)

✍️ Now, we have know that

• Each animal have 4 legs .

• And each human visitor have 2 legs .

✯ So,

• Total no. of animals leg = 4X

• And total no. of human visitors leg = 2Y

✯ According to the question,

$\orange\star\:\rm{\gray{\underline{\underline{\red{4X\:+\:2Y\:=\:216\:}}}}}$ -----(2)

⭐ Multiple 2 in equation (1), we get

$\rm\green{\implies\:2X\:+\:2Y\:=\:156\:}$ ----(3)

⭐ Substract the equation (3) from the equation(2), we get

$\rm{\implies\:4X\:+\:2Y\:-\:2X\:-\:2Y\:=\:216\:-\:156\:}$

$\rm{\implies\:2X\:=\:60\:}$

$\rm{\implies\:X\:=\:\dfrac{60}{2}\:}$

$\rm{\pink{\implies\:X\:=\:30\:}}$

⭐ Now, putting the value of “ X = 30 ” in the equation (1), we get

$\rm{\implies\:30\:+\:Y\:=\:78\:}$

$\rm{\implies\:Y\:=\:78\:-\:30\:}$

$\rm{\pink{\implies\:Y\:=\:48\:}}$

$\rm\red{\therefore}$ The no. of animals and human visitors in the zoo are 30 and 48 respectively .