5. There are several human beings and several dogs
in a room. One tenth of the humans have lost a
leg. The total numbers of feet are 77. Then the
number of dogs is
(1) Not determinable due to insufficient data
(2) 4
(3) 5
(4) 6
Answers
Given:
Total number of feet = 77
Number of humans that have lost leg = 1/10
To Find:
Number of dogs
Solution:
Let the number of human beings be = x
Le the number of dogs be = y
Therefore, total legs = 2x ( human legs) + 4y ( dog legs)
Human beings that have lost legs = 1/10, thus -
2x + 4y − x/10 =77
19x/10 + 4y = 77
Now, 4y must be natural numbers as they represent the number of legs of humans and dogs. Thus, x must be a 10 multiple for this condition.
Thus,
when x = 10
19. ( 10) /10 + 4y = 77
4y = 58, which is not possible
when, x = 20
19. (20) /10 + 4y = 77
4y = 39 which is not possible
when, x = 30
19. (30) /10 + 4y = 77
4y = 20
y = 20/4
y = 5
when, x = 40
19. (40) /10 + 4y = 77
4y = 1, which is again not possible
Answer: There are five dogs.