To complete a wall, M alone takes 60 percent more time than N alone. If together they complete the wall in 20 days, then how much time will N alone take to complete it?

Correct option is B

Given:
M alone takes 60% more time than N alone.
Together they complete the wall in 20 days.
Formula Used:
The time taken by two people working together is given by:
​$$\frac{1}{\text{Time of M}} + \frac{1}{\text{Time of N}} = \frac{1}{\text{Time taken together}}$$​​
Solution:
Let the time taken by N alone to complete the wall be x days. Then, the time taken by M alone to complete the wall is 1.6x days (since M takes 60% more time than N).
​$$\frac{1}{1.6x} + \frac{1}{x} = \frac{1}{20} \\\ \\\frac{1}{1.6x} + \frac{1}{x} = \frac{1}{20} \\\ \\\Rightarrow \frac{1 + 1.6}{1.6x} = \frac{1}{20} \\\ \\\Rightarrow \frac{2.6}{1.6x} = \frac{1}{20} \\\ \\\Rightarrow 2.6 \times 20 = 1.6x \\\ \\\Rightarrow 52 = 1.6x \\\ \\\Rightarrow x = \frac{52}{1.6} = 32.5 = \frac{65}{2}$$ days​

Alternate Solution:

Time Ratio of M and N = 8 : 5 

Efficiency Ratio of M and N = 5 : 8 

Total Work = (5+8)$$\times 20= 260$$ unit

Time taken by N to complete the same work = $$\frac{260}{8}= \frac{65}{2} \text{days}$$​