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A and B can do a piece of work in 2 days and 42 days, respectively. The number of days [Correct to one decimal place] required to complete the work if both A and B work together is:
9
5.1
3
3
9
Use the product-over-sum rule. When one value is significantly larger than the other, the answer will always be slightly larger than the smaller input value.
A completes work in 2 days. B completes work in 42 days.
Days=A+BA├ЧBтАЛ
Use the product-over-sum rule. When one value is significantly larger than the other, the answer will always be slightly larger than the smaller input value.
Students often misread the 2 days as 20 days or fail to use the correct reciprocal summation formula, leading to calculation errors.
Define Individual Rates
A's rate is 1/2 of the work per day and B's rate is 1/42 of the work per day.
RatetotalтАЛ=21тАЛ+421тАЛ
Calculate Combined Rate
Find a common denominator (42) to add the fractions: (21/42) + (1/42) = 22/42.
RatetotalтАЛ=4222тАЛ=2111тАЛ
Calculate Total Days
The time required is the reciprocal of the total rate: 42/22.
Time=2242тАЛтЙИ1.909
A is correct because the combined work rate yields approximately 1.9 days.
This inverse proportion relationship (Work = Rate ├Ч Time) is fundamental to all pipe and cistern problems in quantitative aptitude.
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