A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is?Options18 hrs24 hrs30 hrs12 hrs
Question
A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is?Options18 hrs24 hrs30 hrs12 hrs
Solution
Let's solve this step by step:
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First, convert the time A and B take together to do the work into hours. 9 hours 36 minutes = 9.6 hours.
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The rate at which A and B work together is 1/9.6 work per hour.
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The rate at which C works is 1/48 work per hour.
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Since A can do as much work as B and C together, the rate at which A works is also 1/9.6 + 1/48 = 1/8 work per hour.
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The rate at which B works is the rate at which A and B work together minus the rate at which A works. So, the rate at which B works is 1/9.6 - 1/8 = 1/24 work per hour.
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Therefore, the time B needs to do the work alone is the reciprocal of B's work rate, which is 24 hours.
So, the correct option is 24 hours.
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