Question

A does half as much work as B in three-fourth of the time. If together they take $18$ days to complete the work, how much time shall B take to do it?

• A. $30$ days
• B. $35$ days
• C. $40$ days
• D. None of these

Answer 1

Answer: (A)

$30$ days

Let B takes x days to do the work.

According to the question

A takes $2\times \frac{3x}{4}=\frac{3x}{2}$

(A+B)s 1 days work=$\frac{1}{18}$

then$\frac{1}{x}+\frac{2}{3x}=\frac{1}{18}$

$\frac{5}{3x}=\frac{1}{18}$

$x=\frac{18\times 5}{3}=30$

Hence B takes 30 days to do work