Given:

Milena and Mashuka can together complete a work in 36 days

Mashuka completed 2/5 part work alone and rest Milena completed alone and total time taken by both of them is 78 days

Mashuka is more efficient than Milena

Formula Used:

Work = efficiency × time

Calculation:

Let efficiency of Mashuka be x

Total work = 36 days 

⇒ Efficiency of Milena and Mashuka = 36/36 = 1 

⇒ Efficiency of Milena = 1 – x

Mashuka's work = (2/5) × 36 

Milena's work = (1 – 2/5) × 36 = (3/5) × 36

Total time = \(\frac{{\frac{2}{5} × 36}}{x} + \;\frac{{\frac{3}{5} × 36}}{{\left( {1 - x} \right)}}\)

\( ⇒ 78 = \;\frac{{\frac{2}{5} × 36}}{x} + \;\frac{{\frac{3}{5} × 36}}{{\left( {1 - x} \right)}}\)

\( ⇒ 39 × 5\; = \;\frac{{\left( {1 - x} \right) × 36 + 54\;\left( x \right)}}{{x\;\left( {1 - x} \right)}}\)

\( ⇒ 36 - 36x + 54x\; = 195\left( {x - {x^2}} \right)\)

\(⇒ 65\;{x^2} - 59x + 12 = 0\)

⇒ x = 4/13 and 3/5 

Here x = 4/13 is not valid because it is given that x > (1 – x)

⇒ x = 3/5

Efficiency of Milena = 1 – 3/5 = 2/5

Time taken by Milena to complete the work alone = \(\frac{{36}}{{\frac{2}{5}}}\,\)days

⇒ 18 × 5 days

⇒ 90 days

∴ 90 days taken by Milena to complete the work alone.