Time and Work
Math MCQs

Question :    If Michael can finish the work in 30 days and Thomas can finish the same work in 46 days, then in how many days both can finish the work together?

Correct Answer  18 ³/₁₉ days or 18.158 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Michael = 30 days

And, the number of days to finish the same work by Thomas = 46 days

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

Here,

∵ In 30 days the work done by Michael = 1

∴ In 1 day, the work done by Michael = ¹/₃₀ part

Similarly,

∵ In 46 days the work done by Thomas = 1

∴ In 1 day, the work done by Thomas = ¹/₄₆ 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

= ¹/₃₀ + ¹/₄₆

= ^{23 + 15}/₆₉₀

= ³⁸/₆₉₀ part of work

= ^{38 ÷ 2}/_{690 ÷ 2} part of work

= ¹⁹/₃₄₅ part of work

This means, in 1 day, ¹⁹/₃₄₅ part of the work is done by Michael and Thomas together.

Now, the number of days required to finish ¹⁹/₃₄₅ part of work by Michael + Thomas working together = 1

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

= ¹/_¹⁹/345

= 1 × ³⁴⁵/₁₉ = ³⁴⁵/₁₉ days

= 18 ³/₁₉ days = or 18.158 days

Thus, Michael and Thomas working together will finish the work in 18 ³/₁₉ days = or 18.158 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 = 30 days

And the number of days required to finish the same work by Thomas = 46 days

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

Here a = 30 days

And, b = 46 days

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

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

= ^{30 × 46}/_{30 + 46} days

= ¹³⁸⁰/₇₆ days

= ^{1380 ÷ 4}/_{76 ÷ 4} = ³⁴⁵/₁₉ days

= 18 ³/₁₉ days or 18.158

Thus, Michael and Thomas together will finish the work in 18 ³/₁₉ days or 18.158 days Answer

Similar Questions

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(2) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(3) If Catherine can finish the work in 100 days and Mason can finish the same work in 105 days, then in how many days both can finish the work together?

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(6) Mark can finish a work in 33 days. Steven can finish the same work in 38 days while Paul can finish the work in 43 days. How long will it take to finish it if they work together?

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(8) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?

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