Question

$A$ and $B$ are working together to complete the work in $6$ days. $A$ working alone, can complete the job in $5$ days less than $B$, working alone. How long would it take $A$ to complete the work alone?

• A. $10$ days
• B. $9$ days
• C. $8$ days
• D. $7$ days

Answer 1

Answer: (A)

$10$ days

$A$ and $B$ are working together to complete the work in $6$ days.
Let $x=$ work required by $A$ to do the job, then
$x+5=$ work required by $B$
Let the completed job $=1$
As per the statement. $\frac{6}{x}+\frac{6}{(x+5)}=1$
Multiply by $x(x+5$), cancel the denominators:
$6(x+5)+6x=x(x+5)$
$6x+30+6x=$ $x^2$ $+5x$
$x^2-7x-30=0$
On factoring, we get
$(x-10)(x+3)=0$
$x=10$ or $x=-3$
$x=10$ days
A will take $10$ days to complete the work alone.