In a field there are some cows and ducks. If the number of heads are 33 and number of legs are 84, then what would be the ratio of the numbers of cows to ducks?

Correct option is B

Given:

• Total number of heads = 33
• Total number of legs = 84
• Each cow has 1 head and 4 legs
• Each duck has 1 head and 2 legs

Let:

• Number of cows = x
• Number of ducks = y

Solution:

Forming equations:

1. From heads:
   x + y = 33 → (Equation 1)
2. From legs:
   4x + 2y = 84 → (Equation 2)

Solving the equations:

From Equation 1:
y = 33 − x

Substitute into Equation 2:
4x + 2(33 − x) = 84
4x + 66 − 2x = 84
2x = 18
x = 9 => y = 24

Ratio of cows to ducks = x : y = 9 : 24 = 3 : 8

But the options are reversed — they're asking for cows to ducks, and none match 3:8
So let's double-check.

Wait — we made a mistake!

Let’s re-calculate again:

4x + 2y = 84
x + y = 33
Multiply (x + y = 33) by 2:
2x + 2y = 66

Now subtract from 4x + 2y = 84:
(4x + 2y) − (2x + 2y) = 84 − 66
2x = 18 => x = 9
Then y = 24

Ratio of cows to ducks = 9 : 24 = 3 : 8

Final Answer:

S. Ans. (B) 3/8