Question

If A and B can do a piece of work together in 12 days and B alone can do the same work in 36 days, then find the time taken by A alone to complete the work.

• A. 24 days
• B. 18 days
• C. 20 days
• D. 30 days
• E. None of these

Answer 1

The correct option is B 18 days

Let the time taken by A alone be ‘x’ days.

Total work = L.C.M of x and 36 = 36x units

$A^{\prime }s1-daywork=\frac{36x}{x}=36units$

$B^{\prime }s1-daywork=\frac{36x}{36}=xunits$

(A + B)’s 1-day work = (36 + x) units

According to the question,

$\frac{36x}{(36+x)}=12$

⇒ 36x = 12 × 36 + 12x

⇒ x = 18

So, A alone can do the work in 18 days.