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Examoogle • User • info@examoogle.com • EE-2024-8821
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35 men can do a piece of work in 48 days. The number of men required to complete the same work in 21 days is:
72
80
77
79
80
Use the inverse proportionality relation: M1 × D1 = M2 × D2. Simply calculate (35 × 48) / 21. By simplifying, (35/7) × (48/3) = 5 × 16 = 80.
Number of men (M1) = 35, Time taken (D1) = 48 days. Required time (D2) = 21 days.
M1×D1=M2×D2
Use the inverse proportionality relation: M1 × D1 = M2 × D2. Simply calculate (35 × 48) / 21. By simplifying, (35/7) × (48/3) = 5 × 16 = 80.
Students often mistakenly divide the total work by the number of men and multiply by time, losing track of the inverse relationship between workers and days.
Identify the relation
Since the total work remains the same, the product of the number of men and the number of days must be constant.
M1×D1=M2×D2
Substitute given values
Plug the known values into the equation: 35 men × 48 days = M2 men × 21 days.
35×48=M2×21
Solve for M2
Isolate M2 by dividing both sides by 21: M2 = (35 × 48) / 21.
M2=2135×48
Simplify and Calculate
Divide 35 and 21 by their common factor 7: (5 × 48) / 3 = 5 × 16 = 80.
M2=80
B is correct because the calculation yields 80 men required to finish the work in 21 days.
This concept of inverse proportion is identical to 'Pipes and Cisterns' problems where the number of pipes is inversely proportional to the time taken to fill a tank.
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