Time and Work
MCQs Math


Question:     If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 31 days, then in how many days both can finish the work together?


Correct Answer  14 42/59 days or 14.712 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Anthony = 28 days

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

Thus, the number of days to finish the work by Anthony and Jeffrey together = ?

Here,

∵ In 28 days the work done by Anthony = 1

∴ In 1 day, the work done by Anthony = 1/28 part

Similarly,

∵ In 31 days the work done by Jeffrey = 1

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

Now, in 1 day, the work done by Anthony and Jeffrey together

= In 1 day work done by Anthony + In 1 day the work done by Jeffrey

= 1/28 + 1/31

= 31 + 28/868

= 59/868 part of work

This means in 1 day, 59/868 part of work is done by Anthony and Jeffrey working together.

Now, the number of days required to finish 59/868 part of work by Anthony + Jeffrey working together = 1

∴ the number of days required to finish 1 work by Anthony + Jeffrey together

= 1/59/868

= 1 × 868/59 = 868/59 days

= 14 42/59 days = or 14.712 days

Thus, Anthony and Jeffrey working together will finish the work in 14 42/59 days = or 14.712 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 Anthony = 28 days

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

Thus, the number of days required to finish the work Anthony and Jeffrey working together = ?

Here a = 28 days

And, b = 31 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Anthony and Jeffrey working together

= 28 × 31/28 + 31 days

= 868/59 days

= 14 42/59 days or 14.712

Thus, Anthony and Jeffrey together will finish the work in 14 42/59 days or 14.712 days Answer


Similar Questions

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(2) If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?

(3) Rebecca can finish a work in 58 days. Laura can finish the same work in 63 days while Cynthia can finish the work in 68 days. How long will it take to finish it if they work together?

(4) If Jacob can finish the work in 65 days and Noah can finish the same work in 70 days, then in how many days both can finish the work together?

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(6) If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?

(7) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?

(8) Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?

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