Question

One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?

A. 37 humans and 98 horses

B. 24 horses and 50 humans

C. 31 horses and 74 humans

D. 24 humans and 50 horses

Answer 1

_______Heyy Buddy ❤________

______Here's your Answer _______

Let the number of horse be x and number of Human be y.

A.T.Q.

x + y = 74. ---------(1)

2x + 4y = 196 -----------(2)

Multiplying eq 1 by 2.

=> 2x + 2y = 148. ----------(3).

By elimination method,

=> 2y = 48

=> y = 24.

=> Number of Horse = 24 Horses.

So,

Only Option B has 24 Horses.

=> Option B.
✔✔✔

Answer 2

$\textsf{Let the Number of Humans in the Racing area be : P}$

$\textsf{Let the Number of Horses in the Racing area be : Q}$

$\textsf{Given : The Number of Heads the Person counted = 74}$

$\textsf{We know that : Humans and Horses have only One Head}$

$\textsf{So,The Number of Heads counted by the person should be Equal to Sum of}\\\textsf{Humans and Horses present in the Racing area}$

$\sf{\implies P + Q = 74\;-------\;[1]}$

$\textsf{Given : The Number of Legs the Person counted = 196}$

$\textsf{We know that : Humans have Two Legs and Horses have Four Legs each}$

$\sf{It\;means\;2 \times (Number\;of\;Humans) + 4 \times (Number\;of\;Horses)\;should\;be\;equal\;to}\\\textsf{Total Number of Legs in the Racing area}$

$\sf{\implies 2P + 4Q = 196}$

$\sf{\implies P + 2Q = 98\;------\;[2]}$

$\textsf{Subtracting Equation [1] from Equation [2], We get :}$

$\sf{\implies (P + 2Q) - (P + Q) = 98 - 74}$

$\sf{\implies P + 2Q - P - Q = 24}$

$\sf{\implies Q = 24}$

$\implies \textsf{Number of Horses in the Racing area = 24}$

$\textsf{Substituting Q = 24 in Equation [1], We get :}$

$\sf{\implies P + 24 = 74}$

$\sf{\implies P = 74 - 24}$

$\sf{\implies P = 50}$

$\implies \textsf{Number of Humans in the Racing area = 50}$

$\bf{\underline{Answer} : 24\;Horses\;and\;50\;Humans}$