A can complete a work in 20 days and B in 30 days. They start together but A leaves after 4 days. In how many total days will the work be completed? MCQ with Answer and Explanation
A can complete a work in 20 days and B in 30 days. They start together but A leaves after 4 days. In how many total days will the work be completed?
A. 20 days
B. 16 days
C. 24 days
D. 25 days
Answer: Option C
Solution (By JKSSB Mock Tests)
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.
Explanation:
Let efficiency of B = 100, then efficiency of A = 140. Ratio of efficiency of A : B = 140 : 100 = 7 : 5. Total work = Efficiency of B * Time of B = 5 * 14 = 70 units. Time taken by A alone = 70 / 7 = 10 days.
A can do a work in 14 days and B in 21 days. They begin together but 3 days before the completion of the work, A leaves. What is the total number of days taken to complete the work?
Explanation:
Total work = LCM(14, 21) = 42 units. Efficiency of A = 3, B = 2. Let total days be x. A works for (x - 3) days and B works for x days. 3(x - 3) + 2x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.
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