Q1. A and B can do a piece of work in 45 days and 40 days respectively. They began to work together, but A leaves after m days and B finishes the remaining work in (m + 14) days. The value of m is:
A 9 days Correct
B 23 days
C 5 days
D 17 days
Explanation
A completes 1/45 of the work per day and B completes 1/40 per day. For the first m days both work, so the completed part is m(1/45 + 1/40). After A leaves, B works alone for (m + 14) days, adding (m + 14)/40. Thus m/45 + m/40 + (m + 14)/40 = 1. Multiplying by 360 gives 8m + 9m + 9m + 126 = 360, so 26m = 234 and m = 9. The values 23, 5 and 17 do not satisfy the work equation.