Time and Work
MCQs Math


Question:     If Betty can finish the work in 27 days and Jason can finish the same work in 31 days, then in how many days both can finish the work together?


Correct Answer  14 25/58 days or 14.431 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Betty = 27 days

And, the number of days to finish the same work by Jason = 31 days

Thus, the number of days to finish the work by Betty and Jason together = ?

Here,

∵ In 27 days the work done by Betty = 1

∴ In 1 day, the work done by Betty = 1/27 part

Similarly,

∵ In 31 days the work done by Jason = 1

∴ In 1 day, the work done by Jason = 1/31 part

Now, in 1 day, the work done by Betty and Jason together

= In 1 day work done by Betty + In 1 day the work done by Jason

= 1/27 + 1/31

= 31 + 27/837

= 58/837 part of work

This means in 1 day, 58/837 part of work is done by Betty and Jason working together.

Now, the number of days required to finish 58/837 part of work by Betty + Jason working together = 1

∴ the number of days required to finish 1 work by Betty + Jason together

= 1/58/837

= 1 × 837/58 = 837/58 days

= 14 25/58 days = or 14.431 days

Thus, Betty and Jason working together will finish the work in 14 25/58 days = or 14.431 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 Betty = 27 days

And the number of days required to finish the same work by Jason = 31 days

Thus, the number of days required to finish the work Betty and Jason working together = ?

Here a = 27 days

And, b = 31 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Betty and Jason working together

= 27 × 31/27 + 31 days

= 837/58 days

= 14 25/58 days or 14.431

Thus, Betty and Jason together will finish the work in 14 25/58 days or 14.431 days Answer


Similar Questions

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(2) If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?

(3) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?

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(5) If Mark can finish the work in 30 days and Jacob can finish the same work in 33 days, then in how many days both can finish the work together?

(6) If Susan can finish the work in 15 days and Donald can finish the same work in 18 days, then in how many days both can finish the work together?

(7) If Alexander can finish the work in 91 days and Wayne can finish the same work in 96 days, then in how many days both can finish the work together?

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(9) If Myra can finish the work in 15 days and Sophia can finish the same work in 20 days, then in how many days they both can finish the work working together?

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