Time and Work
Math MCQs

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 & 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

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