Q88
ArithmeticAlgebra, Equations & Operations
In an enclosure, there are crows as well as cows. If there are 30 heads and 100 legs, what is the ratio of the cows to crows?
- a.1:2
- b.1:3
- c.2:1
- d.3:1
Answer: (C) 2:1
Let cows $= x$ and crows $= y$. Heads: $x + y = 30$. Legs: $4x + 2y = 100$. Subtracting twice the first equation from the second gives $2x = 40$, so $x = 20$ cows and $y = 10$ crows, a ratio of $20 : 10 = 2 : 1$. Shortcut: if all 30 were crows there would be 60 legs; the 40 extra legs come from cows at 2 extra legs each, so there are 20 cows. The trap is option A (1 : 2), which is the ratio of crows to cows; always check the order asked in the question.