S1 alone can do a work in 16 days and S2 alone can do the same work in 80 days. With help of S3, they finish the same work in 6 days. In how many days S3 alone can do the same work?

Correct option is C

Given:
S1 can complete the work in 16 days.
S2 can complete the work in 80 days.
Together with S3, they complete the work in 6 days.
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Formula Used:
Work done together = (1/S1) + (1/S2) + (1/S3) = 1/6.
S1 = 16 days, S2 = 80 days, Together = 6 days.

Solution:
We use the equation for work done together:
(1/16) + (1/80) + (1/S3) = 1/6
Solve for 1/S3:
(1/S3) = 1/6 - (1/16 + 1/80)
(1/S3) = 1/6 - (5/80 + 1/80)
(1/S3) = 1/6 - 6/80
(1/S3) = 1/6 - 3/40
(1/S3) = (40 - 18) / 240
(1/S3) = 22/240
S3 = 240/22 = 120/11 days