Robin and Varun together can paint a hall in 6 days. Robin alone can paint it in 42 days. In how many days can Varun alone paint it?​

Correct option is A

Given:

Robin + Varun finish in 6 days

Robin alone finishes in 42 days

Solution:
Combined rate $$= \frac{1}{6}$$​​

Robin’s rate $$= \frac{1}{42}$$​

Varun’s rate =$$\frac{1}{6} - \frac{1}{42} = \frac{7 - 1}{42} = \frac{6}{42} = \frac{1}{7}$$​​

Therefore, Varun’s time = $$\frac{1}{\frac17}$$​ = 7 days.

Alternate Method:
Assume total work = LCM(6, 42) = 42 units.

Combined does $$\frac{42}6$$​ = 7 units/day.

Robin does $$\frac{42}{42}$$​ = 1 unit/day.

Varun does 7 - 1 = 6 units/day

time =$$\frac{42}6$$​ = 7 days.