Question

To complete a work. A takes $$50 %$moretimethan$B$.Iftogethertheytake$18$daystocompletethework,howmuchtimeshall$B$ take to do it?

• A. $30$ days
• B. $35$ days
• C. $40$ days
• D. $45$ days

Answer 1

Answer: (A)

$30$ days

Let us consider the number of days $B$ requires to complete the work $=x$ days

So, number of days $A$ requires to complete the work $=x+\left(50/100\right)x=1.5x$

$\therefore$ We can calculate, work done by $A$ in $1$ day $=1/1.5x=2/3x$

And work done by $B$ in $1$ day $=1/x$

We know that the Number of days $A$ and $B$ together requires to do work $=18$ days

So, work done by both $A$ and $B$ in $1$ day $=1/18$

$\therefore 2/3x+18x=1/18$
$5/3x=1/18$
$x=(5\times 18)/3$

$x=30$

$\therefore B$ requires $30$ days to complete the work.