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Question 119
Tom, Suresh and Adil are capable of finishing a task in 2, 4 and 8 hours, respectively. Suresh takes a magic medicine that increases his power by n times. Suresh works together with Tom and Adil to complete the task in less than 1 hour. Find the value of the expression $$n^2 + 2$$ where n is a positive integer.
Solution
Let us assume that the total is 8 units (LCM of 2,4,8).
This means Tom does 4 units/hour, Suresh does 2 units/hour, and Adil does 1 unit/hour.
Now, Suresh's efficiency is increased and becomes 2n units/hour.
Due to this, they all complete the 8 units of work in less than 1 hour.
This means, $$\ \ \frac{\ 8}{5+2n}<1\ $$, or n>1.5
The nearest integer is 2, making the value of $$n^2 + 2$$ as 6
