# Time & Work Problems

Let’s consider that a  person X can finish a particular work in N days. Then, work done by A in 1 day = 1/Nᵗʰ part of the work. Suppose that the work done by X in 1 day is 1N. Then, time taken by X to finish the whole work = N days.

Example:

Ajith alone can finish a piece of work in 12 days and Binoy alone can do it in 15 days. If both of them work at it together, how much time will they take to finish it?

Solution:

Time taken by Ajith to finish the work = 12 days.

Work done by Ajith in 1 day = ¹/₁₂

Time taken by Binoy to finish the work = 15 days.

Work done by Binoy in 1 day = ¹/₁₅

Work done by (Ajith + Binoy) in 1 day = ¹/₁₂ + ¹/₁₅ = ⁹/₆₀ = ³/₂₀

Time taken by (Ajith + Binoy) to finish the work = 20/6 days, i.e., 6²/₃ days.

Hence both can finish the work in 6²/ days.

2. Alia and Cathy together can do a piece of work in 15 days, while Cathy alone can finish it 20 days. In how many days can Alia alone finish the work?

Solution:

Time taken by (Alia + Cathy) to finish the work = 15 days.

Time taken by Cathy alone to finish the work 20 days. (Alia + Cathy)’s 1 day’s work = ¹/₁₅

and Cathy’s 1 day’s work = ¹/₂₀

Alia’s 1 day’s work = {(Alia + Cathy)’s 1 day’s work} - {Cathy’s 1 day’s work}

= (¹/₁₅ - ¹/₂₀) = (4 - 3)/60 = ¹/₆₀

Therefore, Alia alone can finish the work in 60 days.