Question

A and B separately do a work in 10 and 15 days respectively they work together for some days and then A completed the remaining work in 5 days for how many days Had A and B work together

Answer 1

A CAN COMPLETE THE WORK IN 10 DAYS,
SO, A's 1 DAY WORKING CAPACITY =
$\frac{1}{10}$
AND,
B CAN COMPLETE THE WORK IN 15 DAYS,
SO, B's 1 DAY WORKING CAPACITY =
$\frac{1}{15}$
SO,
IF A AND B BOTH WILL WORK TOGETHER...
THEIR 1 DAY WORKING CAPACITY =
$\frac{1}{10 } + \frac{1}{15} \\ = \frac{3 + 2}{30} \\ = \frac{5}{30} \\ = \frac{1}{6}$
SO, LET TAKE THE TOTAL WORK AS '1'.....
SO, LET THE TOTAL DAYS IN WHICH A AND B BOTH HAVE WORKDE BE x.....
SO, WORK THEY HAVE DONE IN x DAYS =
x × Their working capacity of a day =
$x \times \frac{1}{6} \\ = \frac{x}{6}$
AND, A HAS WORKED 5 DAYS ALONE.....
SO, HIS WORK OF 5 DAYS =
5 × A's 1 DAY WORKING CAPACITY =
$5 \times \frac{1}{10} \\ = \frac{1}{2}$
SO, IF TOTAL WORK IS = 1
SO,
BOTH OF THEIR WORK + A's 5 DAY WORK = 1
SO, A/Q;
$\frac{x}{6} + \frac{1}{2} = 1 \\ = > \frac{x + 3}{6} = 1 \\ = > x + 3 = 1 \times 6 \\ = > x = 6 - 3 \\ = > x = 3$
HENCE, A AND B HAVE WORKED TOGETHER FOR 3 DAYS!....

THERE YOU GO!!!.....