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Vikas takes thrice as much times as Ronit and Ronit takes thrice as much as Vineet to finish a piece of work. Vikas and Ronit working together, they can finish the work in 18 days. In how many days Vineet alone can do same work?

Vikas takes thrice as much times as Ronit and Ronit takes thrice as much as Vineet to finish a piece of work. Vikas and Ronit working together, they can finish the work in 18 days. In how many days Vineet alone can do same work? Correct Answer 8 days

Given:
Time taken by Vikas = 3 × Time taken by Ronit
Time taken by Ronit = 3 × Time taken by Vineet
No. of days required by Vikas and Ronit together = 18 days

Concept used:
Total work = No. of days × Efficiency of work
Ratio of time is inversely proportional to ratio of efficiency.

Calculation:
Let the time taken by Vineet be x.
Time taken by Ronit = 3x
Time taken by Vikas = 9x
Ratio of time of Vikas, Ronit and Vineet = 9x : 3x : x = 9 : 3 : 1
Ratio of efficiency Vikas, Ronit and Vineet = 1/9 : 1/3 : 1/1
Ratio of efficiency Vikas, Ronit and Vineet = 1 : 3 : 9 
Total work = (x + 3x) × 18
⇒ 4x × 18
⇒ 72
Time taken by Vineet = 72x/9x
⇒ 8
∴ Vineet can do the work alone in 8 days.

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