Time and Work
MCQs Math


Question:     If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?


Correct Answer  6 14/27 days or 6.519 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Michael = 11 days

And, the number of days to finish the same work by Thomas = 16 days

Thus, the number of days to finish the work by Michael and Thomas together = ?

Here,

∵ In 11 days the work done by Michael = 1

∴ In 1 day, the work done by Michael = 1/11 part

Similarly,

∵ In 16 days the work done by Thomas = 1

∴ In 1 day, the work done by Thomas = 1/16 part

Now, in 1 day, the work done by Michael and Thomas together

= In 1 day work done by Michael + In 1 day the work done by Thomas

= 1/11 + 1/16

= 16 + 11/176

= 27/176 part of work

This means in 1 day, 27/176 part of work is done by Michael and Thomas working together.

Now, the number of days required to finish 27/176 part of work by Michael + Thomas working together = 1

∴ the number of days required to finish 1 work by Michael + Thomas together

= 1/27/176

= 1 × 176/27 = 176/27 days

= 6 14/27 days = or 6.519 days

Thus, Michael and Thomas working together will finish the work in 6 14/27 days = or 6.519 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 Michael = 11 days

And the number of days required to finish the same work by Thomas = 16 days

Thus, the number of days required to finish the work Michael and Thomas working together = ?

Here a = 11 days

And, b = 16 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Michael and Thomas working together

= 11 × 16/11 + 16 days

= 176/27 days

= 6 14/27 days or 6.519

Thus, Michael and Thomas together will finish the work in 6 14/27 days or 6.519 days Answer


Similar Questions

(1) If Sarah can finish the work in 19 days and Joshua can finish the same work in 22 days, then in how many days both can finish the work together?

(2) If Kimberly can finish the work in 38 days and Stephen can finish the same work in 43 days, then in how many days both can finish the work together?

(3) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?

(4) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?

(5) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?

(6) Janet can finish a work in 98 days. Maria can finish the same work in 103 days while Heather can finish the work in 108 days. How long will it take to finish it if they work together?

(7) If Barbara can finish the work in 35 days and Anthony can finish the same work in 51 days, then in how many days both can finish the work together?

(8) Ashley can finish a work in 32 days. Kimberly can finish the same work in 33 days while Emily can finish the work in 34 days. How long will it take to finish it if they work together?

(9) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

(10) Karen can finish a work in 24 days. Nancy can finish the same work in 29 days while Betty can finish the work in 34 days. How long will it take to finish it if they work together?


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