Tanks can be built by masons in 12 hours. After laboring for 6 hours, he enlisted a boy's assistance and completed the task in an additional 5 hours. The amount of time it will take the boy to finish the work on their own?

Given:

Time for mason alone to build the tank = 12 hours.

Mason worked alone for 6 hours.

Mason and boy together completed the remaining work in 5 hours.

Formula Used:

Work = Efficiency × Time

Efficiency = Work / Time

Let the total work be W.

Efficiency of the mason = Work / Time = W / 12 (work per hour)

Let the efficiency of the boy = E_b (work per hour)

Calculations:

Work done by the mason in the first 6 hours = Efficiency of mason × Time

Work done by the mason = (W / 12) × 6 = 6W / 12 = W / 2

Remaining work = Total Work - Work done by mason = W - W / 2 = W / 2

The remaining work (W / 2) was completed by the mason and the boy together in 5 hours.

Combined efficiency of mason and boy = Efficiency of mason + Efficiency of boy

Combined efficiency = (W / 12) + E_b

Work done by mason and boy together = Combined efficiency × Time

W / 2 = ((W / 12) + E_b) × 5

W / 2 = (5W / 12) + 5E_b

To find E_b, rearrange the equation:

5E_b = W / 2 - 5W / 12

5E_b = 6W / 12 - 5W / 12

5E_b = W / 12

E_b = W / (12 × 5) = W / 60

The efficiency of the boy is W / 60 (work per hour).

Time taken by the boy to finish the work alone = Total Work / Efficiency of boy

Time taken by the boy = W / (W / 60) = W × (60 / W) = 60 hours.

∴ The boy will take 60 hours to finish the work on their own.