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

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