A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start together but C leaves 4 days before the completion of the work. In how many days was the work completed? MCQ with Answer and Explanation
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start together but C leaves 4 days before the completion of the work. In how many days was the work completed?
A. 10 days
B. 12 days
C. 13 days
D. 11 days
Answer: Option D
Solution (By JKSSB Mock Tests)
Total work = LCM(24, 30, 40) = 120 units. Efficiency of A = 5, B = 4, C = 3. Let the total number of days be x. A and B work for x days, while C works for (x - 4) days. 5x + 4x + 3(x - 4) = 120 => 12x - 12 = 120 => 12x = 132 => x = 11 days.
Explanation:
Let B's efficiency = 1, then A's efficiency = 3. Combined efficiency = 3 + 1 = 4. Total work = 18 * 4 = 72 units. Time taken by A alone = 72 / 3 = 24 days.
If 12 men and 16 boys can do a piece of work in 5 days; while 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. In 4 days, work completed = 4 * (3 + 2) = 20 units. Remaining work = 60 - 20 = 40 units. Time taken by B to finish remaining work = 40 / 2 = 20 days. Total days = 4 + 20 = 24 days.
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