Question

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​

Answer 1

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.