X and Y can do a piece of work in 45 days and 40 days respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to?

Explanation

Let total work be \text{LCM}(45, 40) = 360 units. Efficiency of X = 8, Y = 9. Y alone finishes 23 \times 9 = 207 units. Remaining work 360 - 207 = 153 units was done by X and Y together. So, n = \frac{153}{8 + 9} = 9 days.

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