​Sony and Mary can complete a painting in 4 days and 6 days, respectively. They work on same painting on alternate days starting with Mary. In how many days will they together complete the painting?

Correct option is C

Given:

Sony can complete in 4 days;

Mary can complete in 6 days

Formula Used:

Work done in two days = $$\text{Mary's efficiency} + \text{Sony's efficiency}$$​​

Solution:

Sony 's efficiency = $$\frac{1}{4}$$​​

Mary's  efficiency = $$\frac{1}{6}$$​​

Work in two days: $$\frac{1}{6} + \frac{1}{4} = \frac{2 + 3}{12} = \frac{5}{12}$$​​

​$$\text{Complete cycles} = \frac{1}{\frac{5}{12}} = 2$$​​

Work done in 4 days  $$2 \times \frac{5}{12} = \frac{10}{12} = \frac{5}{6}$$​​

Remaining work: $$1 - \frac{5}{6} = \frac{1}{6}$$​​

Mary's day for $$\frac{1}{6}$$​ work:

​$$\text{Time} = \frac{\text{Work}}{\text{Efficiency}} = \frac{\frac{1}{6}}{\frac{1}{6}} = 1$$​​

​$$Total \ time = 4+1=5 days$$​​