​Ayush and Bilal can do a job in ‘D’ days. If Ayush can alone do the job in D+3 days and Bilal alone can do the job in D+12 days, find the value of D.​

Correct option is C

Given:
Ayush and Bilal together do a job in D days
Ayush alone takes D + 3 days
Bilal alone takes D + 12 days
We are to find the value of D

Solution:
Let work = 1 unit (total job)
Work = Rate × Time
So,

​$$\frac{1}{D} = \frac{1}{D + 3} + \frac{1}{D + 12} \\\ \\\frac{1}{D} = \frac{(D + 12) + (D + 3)}{(D + 3)(D + 12)} = \frac{2D + 15}{(D + 3)(D + 12)} \\\ \\\Rightarrow D(2D + 15) = (D + 3)(D + 12) \\\ \\\Rightarrow 2D^2 + 15D = D^2 + 15D + 36 \\\ \\\Rightarrow D^2 = 36 \Rightarrow D = 6 \\$$

Final Answer:
D = 6 ​​