Correct Answer - Option 3 : 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.