Question

A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?

• A. 4 days
• B. 6 days
• C. 8 days
• D. 10 days

Answer 1

Answer:

B. 6 days

Let, B alone can complete the work in be x days

According to the question,

$\frac{1}{12}+\frac{1}{x} = \frac{1}{4}$

⇒ $\frac{1}{x} =\frac{1}{4}-\frac{1}{12}$

⇒ $\frac{1}{x} = \frac{(3-1)}{12}$

⇒ $\frac{1}{x} =\frac{1}{6}$

⇒ x = 6

∴ B alone can complete the work in 6 days

Alternate Solution

Let total work done be 12 units (LCM of 4 and 12)

Hence,

Efficiency of A + B = $\frac{12}{4} = 3 units/day$

Efficiency of A = $\frac{12}{12} = 1 unit/day$

Now, efficiency of B = 3 - 1 = 2 units/day

∴ Required days = Total work/Efficiency of B = $\frac{12}{2} = 6 days$