A can complete a work in 27 days and B in 37 days. If both work together, in how many days will the work be completed? MCQ with Answer and Explanation
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Question #1
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A can do a piece of work in 14 days and B in 21 days. They begin together but 3 days before the completion of the work, A leaves. The total number of days taken to complete the work is:
Correct Answer: Option B
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) + 2*x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.
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) + 2*x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.
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Maths
Time and Work
Question #2
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A, B and C together can earn Rs. 300 per day, while A and C together can earn Rs. 188 and B and C together can earn Rs. 152. Find the daily earning of C.
Correct Answer: Option A
Explanation:
Given: A + B + C = 300, A + C = 188, B + C = 152. Substitute A + C in the first equation: 188 + B = 300 => B = 112. Now substitute B in B + C = 152: 112 + C = 152 => C = 40. Thus, C's earning is Rs. 40.
Given: A + B + C = 300, A + C = 188, B + C = 152. Substitute A + C in the first equation: 188 + B = 300 => B = 112. Now substitute B in B + C = 152: 112 + C = 152 => C = 40. Thus, C's earning is Rs. 40.
This question belongs to:
Maths
Time and Work
Question #3
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A is 40% more efficient than B. If they together can finish a work in 10 days, in how many days can A alone finish it?
Correct Answer: Option A
Explanation:
Let efficiency of B = 5, then efficiency of A = 7. Combined efficiency = 12 units/day. Total work = 10 * 12 = 120 units. Time taken by A alone = 120 / 7 = 17(1/7) days.
Let efficiency of B = 5, then efficiency of A = 7. Combined efficiency = 12 units/day. Total work = 10 * 12 = 120 units. Time taken by A alone = 120 / 7 = 17(1/7) days.
This question belongs to:
Maths
Time and Work
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