Question

Tick (✓) the correct answer:
To complete a work, A takes 50% more time than B. 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) 45 days

Answer 1

(a) 30 days

$$\begin{gathered} LetB\hspace{0.17em}takexdaystocompletethework. \\ ThenAtakes\left(x+\frac{50}{100}x\right)=1.5x \\ A\text{'}s1day\text{'}swork=\frac{1}{1.5x}=\frac{2}{3x} \\ B\text{'}s1day\text{'}swork=\frac{1}{x} \\ (A+B)\hspace{0.17em}takes18daystocompletethework. \\ (A+B)\text{'}s1day\text{'}snetwork=\frac{1}{18} \\ or\frac{1}{18}=\frac{2}{3x}+\frac{1}{x} \\ \Rightarrow \frac{1}{18}=\frac{5}{3x} \\ Bycross-multiplication,weget: \\ x=30days \\ \therefore Balonewilltake30daystocompletethework. \end{gathered}$$