Word Problem 21
Problem 21: There are some pigeons and hares in a zoo. If heads are counted, these are 200. If legs are counted, they are 580. The number of hares in the zoo are ;
a) 50 b) 150 c) 90 d) 120
Solution:
We are given following information;
Heads = 200
Legs = 580
Hares = ?
Pigeons = ?
We suppose that ;
Number of Hares = y
Number of Pigeons = z
Before we proceed further, keep in mind that each hare has four legs — and each pigeon has two legs !
So, total number of heads is equal to total number of hares and pigeons which is 200
so,
\[ z+y=200——–(1) \]
Each pigeons has 2 legs – means z pigeons will have 2z legs. Similarly each hare has 4 legs — means y hares will have 4y legs ! But total legs are 580;
So
\[ 2z+4y=580 ——– (2) \]
Multiplying eq (1) with 2 w get,
\[ 2z+2y=400 ——(3) \]
Subtracting eq (3) from eq(2) we get;
\[ 2y=180 \]
finally,
\[ y=\frac{180}{2}=90 \]
Since y is number of heads of hares – so number of hares is 90
Copyright secured by Digiprove © 2020-2021