Time and Work
MCQs Math


Question:     If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?


Correct Answer  48 42/193 days or 48.218 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Rachel = 94 days

And, the number of days to finish the same work by Roy = 99 days

Thus, the number of days to finish the work by Rachel and Roy together = ?

Here,

∵ In 94 days the work done by Rachel = 1

∴ In 1 day, the work done by Rachel = 1/94 part

Similarly,

∵ In 99 days the work done by Roy = 1

∴ In 1 day, the work done by Roy = 1/99 part

Now, in 1 day, the work done by Rachel and Roy together

= In 1 day work done by Rachel + In 1 day the work done by Roy

= 1/94 + 1/99

= 99 + 94/9306

= 193/9306 part of work

This means in 1 day, 193/9306 part of work is done by Rachel and Roy working together.

Now, the number of days required to finish 193/9306 part of work by Rachel + Roy working together = 1

∴ the number of days required to finish 1 work by Rachel + Roy together

= 1/193/9306

= 1 × 9306/193 = 9306/193 days

= 48 42/193 days = or 48.218 days

Thus, Rachel and Roy working together will finish the work in 48 42/193 days = or 48.218 days Answer

Shortcut Trick to solve the problems based on time and work using formula

Case: If A can finish a work in a days, and B can finish the same work in b days,
then working together the number of days require to finish the work
= a × b/a + b days.

Here given,

The number of days required to finish the work by Rachel = 94 days

And the number of days required to finish the same work by Roy = 99 days

Thus, the number of days required to finish the work Rachel and Roy working together = ?

Here a = 94 days

And, b = 99 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Rachel and Roy working together

= 94 × 99/94 + 99 days

= 9306/193 days

= 48 42/193 days or 48.218

Thus, Rachel and Roy together will finish the work in 48 42/193 days or 48.218 days Answer


Similar Questions

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(2) Jason can finish a work in 59 days. Ryan can finish the same work in 64 days while Jacob can finish the work in 69 days. How long will it take to finish it if they work together?

(3) If Donna can finish the work in 39 days and Brandon can finish the same work in 42 days, then in how many days both can finish the work together?

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