Given:

Time taken by A and B to together complete the work = 7 days

Time taken by B and C to together complete the work = 8.75 days

Time taken by A to complete the work alone = 10.5 days

Concept Used:

If a person takes x days to complete a work, the part of the work completed by him in 1 day = 1/x

Calculation:

Part of the work completed by A and B together in 1 day is obtained as:

(1/A) + (1/B) = 1/7      ----(i)

Part of the work completed by B and C together in 1 day is obtained as:

(1/B) + (1/C) = 1/8.75 = 4/35      ----(ii)

Part of the work completed by A alone in 1 day is obtained as:

1/A = 1/10.5 = 2/21       ----(iii)

We substitute the value of (1/A) into equation(i) to obtain:

(2/21) + (1/B) = 1/7

⇒ 1/B = 1/21       ----(iv)

Hence, B takes 21 days to complete the work alone

Now, we substitute the value of (1/B) into equation(ii) to obtain:

(1/21) + (1/C) = 4/35

⇒ 1/C = (4/35) – (1/21) = 1/15

Hence, the time required by C to complete the work alone = 15 days

So, the time C will need to complete double the amount of work will be:

2 × 15 = 30 days

∴ The time C will take to complete double the same amount of work, when working alone, will be 30 days