AFCAT II 24 Aug 2019 Paper

Let Marshall, Randy and Roger have x, y and z numberof coins respectively.
then, According to the question 5x=8y⇒y=

5x

8

and 8x=5z⇒z=

8x

5

As y is integer, then , for y=

5x

8

for x = 8 ; y=

5×8

8

=5 , Again z is integer, for z=

8x

5

for x=5,z=

8×5

5

=8
∴ x = L.C.M of (8, 5) = 40
When x = 40, y = 5 × 5 = 25
and z = 8 × 8 = 64.
∴ Minimum of (x + y + z) = 40 + 25 + 64 = 129.