KVPY SA Exam 2012 Question Paper

Question : 12 of 80

Marks: +1, -0

Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together. On the other hand, working alone, B would need

4 1/2

hours more to complete the work than if both worked together. How much time would they take to complete the job working together?

4 hours
5 hours
6 hours
7 hours

Validate

Solution:

If A & B work together take time t hr. If A work alone takes t + 8 hr. to complete the work
Work/hr by A is

1/{t+8}.

Similarly for B work/hr is

1/{t+9\/2}

When A & B work together there work/hr

1/{t+8}+1/{t+9\/2}

Work will be done in t hr.

t(1/{t+8}+1/{t+9\/2})=1

By solving
t = 6

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