X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 14 days, Y alone can finish that work in: MCQ with Answer and Explanation
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Question #1
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A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started together but A left 2 days after the start and B left 3 days before the completion of the work. How long did the work last?
Correct Answer: Option B
Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let total days be x. A works for 2 days. B works for (x - 3) days. C works for x days. Total work = 2*6 + (x - 3)*5 + 4*x = 60 => 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let total days be x. A works for 2 days. B works for (x - 3) days. C works for x days. Total work = 2*6 + (x - 3)*5 + 4*x = 60 => 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
This question belongs to:
Maths
Time and Work
Question #2
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A can do a work in 18 days and B in 28 days. They work together for 5 days. What percentage of work remains?
Correct Answer: Option A
Explanation:
Remaining work = (1 - 5*(1/18+1/28)) ×100 = 54.37%.
Remaining work = (1 - 5*(1/18+1/28)) ×100 = 54.37%.
This question belongs to:
Maths
Time and Work
Question #3
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A and B can do a piece of work in 10 days and 15 days respectively. They work together for 2 days and then A is replaced by C. The work is finished in next 4 days. In how many days can C alone finish the work?
Correct Answer: Option A
Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In 2 days, A and B do 2 * (3 + 2) = 10 units. Remaining work = 30 - 10 = 20 units. This is completed by B and C in 4 days, so combined efficiency of B and C = 20 / 4 = 5 units/day. Since efficiency of B = 2, efficiency of C = 5 - 2 = 3 units/day. Time taken by C alone = 30 / 3 = 10 days.
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In 2 days, A and B do 2 * (3 + 2) = 10 units. Remaining work = 30 - 10 = 20 units. This is completed by B and C in 4 days, so combined efficiency of B and C = 20 / 4 = 5 units/day. Since efficiency of B = 2, efficiency of C = 5 - 2 = 3 units/day. Time taken by C alone = 30 / 3 = 10 days.
This question belongs to:
Maths
Time and Work
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