Time and Work
Math MCQs

Question :    If Michael can finish the work in 8 days and Thomas can finish the same work in 11 days, then in how many days both can finish the work together?

Correct Answer  4 ¹²/₁₉ days or 4.632 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Michael = 8 days

And, the number of days to finish the same work by Thomas = 11 days

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

Here,

∵ In 8 days the work done by Michael = 1

∴ In 1 day, the work done by Michael = ¹/₈ part

Similarly,

∵ In 11 days the work done by Thomas = 1

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

= ¹/₈ + ¹/₁₁

= ^{11 + 8}/₈₈

= ¹⁹/₈₈ part of work

This means in 1 day, ¹⁹/₈₈ part of work is done by Michael and Thomas working together.

Now, the number of days required to finish ¹⁹/₈₈ part of work by Michael + Thomas working together = 1

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

= ¹/_¹⁹/88

= 1 × ⁸⁸/₁₉ = ⁸⁸/₁₉ days

= 4 ¹²/₁₉ days = or 4.632 days

Thus, Michael and Thomas working together will finish the work in 4 ¹²/₁₉ days = or 4.632 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 = 8 days

And the number of days required to finish the same work by Thomas = 11 days

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

Here a = 8 days

And, b = 11 days

Thus, using formula ^{a × b}/_{a + b} days

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

= ^{8 × 11}/_{8 + 11} days

= ⁸⁸/₁₉ days

= 4 ¹²/₁₉ days or 4.632

Thus, Michael and Thomas together will finish the work in 4 ¹²/₁₉ days or 4.632 days Answer

Similar Questions

(1) Michael can finish a work in 7 days. David can finish the same work in 8 days while William can finish the work in 9 days. How long will it take to finish it if they work together?

(2) 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?

(3) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?

(4) If Barbara can finish the work in 16 days and Anthony can finish the same work in 21 days, then in how many days both can finish the work together?

(5) 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?

(6) Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?

(7) If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?

(8) If Jessica can finish the work in 20 days and Paul can finish the same work in 25 days, then in how many days both can finish the work together?

(9) If Donald can finish the work in 35 days and Nicholas can finish the same work in 40 days, then in how many days both can finish the work together?

(10) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?