Question

A does half as much work as B in three-fourth of the time. If together they take 66 days to complete the work, how many days shall B alone take to do it?

• A. 55
• B. 68
• C. 110
• D. 90

Answer 1

Answer:

C. 110

Let B’s 1 day work = b
Then A’s 1 day work = a

Step 1: Form relation between A and B

Given:
A does half as much work as B in three-fourth of the time.

That means:

Work done by A in ( \frac{3}{4} ) day
= Work done by B in 1 day × ( \frac{1}{2} )

$a \times \frac{3}{4} = \frac{1}{2} b$

Multiply both sides by 4:

$3a = 2b$
$a = \frac{2}{3} b$
Step 2: Combined work rate

$a + b = \frac{2}{3}b + b$
$= \frac{2}{3}b + \frac{3}{3}b$
$= \frac{5}{3}b$

Step 3: They complete work in 66 days

$\frac{5}{3}b = \frac{1}{66}$
$b = \frac{1}{66} \times \frac{3}{5}$
$b = \frac{3}{330}$
$b = \frac{1}{110}$

Step 4: Time taken by B alone

$\text{Time} = \frac{1}{b} = 110 \text{ days}$

Final Answer: B alone will take 110 days.