Question

For doing some work Ganesh takes $10$ days more than John. If both work together they will complete the work in $12$ days. Find the number of days if Ganesh works alone ?

• A. $10$ days
• B. $20$ days
• C. $30$ days
• D. $40$ days

Answer 1

Answer: (C)

$30$ days

Let Ganesh can do work in $x$ days
and John can do work in $y$ days
Then, $x-y=10$

$\therefore x=10+y$
Ganesh's one day work = $\frac{1}{x}$

John's one day work = $\frac{1}{y}$

When they both work together, they complete work in 12 days.
Then, $\frac{1}{x}+\frac{1}{y}=\frac{1}{12}$

$\frac{x+y}{xy}=\frac{1}{12}$

$xy=12(x+y)$
$y(10+y)=12(10+y+y)$
$10y+y^2=120+24y$
$y^2-14y-120=0$

$y=\frac{14\pm \sqrt{196+480}}{2}$

$y=\frac{14\pm 26}{2}$

$y=20,-6$

$x=y+10=20+10=30$ days
Hence, Ganesh can complete work in $30$ days.