A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A left after some days and B finished the remaining work in 23 days. A left after ?

Answer: B. 9 days

The number 360 is the Least Common Multiple (LCM) of 45 and 40.
A's speed = 360 /45 = 8 units/day
B's speed = 360/40 = 9 units/day
B finished the last 23 days of work alone, completing 207 units ( 23 X 9)
This leaves 153 units ( 360-207) that A and B must have completed together.
.Their combined speed is 17 units/day ( 8+9), so they worked together for 9 days ( 153/17)
Since A left as soon as they stopped working together, A left after 9 days.

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