Question

Manish, Rahul and Bharti have some stones with each of them. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?

___

Answer 1

Let the stones with Manish, Rahul and Bharti be m,r and b respectively.

Given, 5r = 7m and 5m = 7b

$\Rightarrow$ 25r = 35m and 35m = 49b

$\Rightarrow$ 25r = 35m = 49b = k

The least possible integral values for r, m, b will be r = 49, m = 35 and b = 25 [Using LCM concept]

Total = 49 + 35 + 25 = 109.