Time and Work
Math MCQs

Question :    If Thomas can finish the work in 18 days and Andrew can finish the same work in 21 days, then in how many days both can finish the work together?

Correct Answer  9 ⁹/₁₃ days or 9.692 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Thomas = 18 days

And, the number of days to finish the same work by Andrew = 21 days

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

Here,

∵ In 18 days the work done by Thomas = 1

∴ In 1 day, the work done by Thomas = ¹/₁₈ part

Similarly,

∵ In 21 days the work done by Andrew = 1

∴ In 1 day, the work done by Andrew = ¹/₂₁ part

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

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

= ¹/₁₈ + ¹/₂₁

= ^{7 + 6}/₁₂₆

= ¹³/₁₂₆ part of work

This means in 1 day, ¹³/₁₂₆ part of work is done by Thomas and Andrew working together.

Now, the number of days required to finish ¹³/₁₂₆ part of work by Thomas + Andrew working together = 1

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

= ¹/_¹³/126

= 1 × ¹²⁶/₁₃ = ¹²⁶/₁₃ days

= 9 ⁹/₁₃ days = or 9.692 days

Thus, Thomas and Andrew working together will finish the work in 9 ⁹/₁₃ days = or 9.692 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 Thomas = 18 days

And the number of days required to finish the same work by Andrew = 21 days

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

Here a = 18 days

And, b = 21 days

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

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

= ^{18 × 21}/_{18 + 21} days

= ³⁷⁸/₃₉ days

= ^{378 ÷ 3}/_{39 ÷ 3} = ¹²⁶/₁₃ days

= 9 ⁹/₁₃ days or 9.692

Thus, Thomas and Andrew together will finish the work in 9 ⁹/₁₃ days or 9.692 days Answer

Similar Questions

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(2) If Christopher can finish the work in 25 days and Brian can finish the same work in 30 days, then in how many days both can finish the work together?

(3) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?

(4) Thomas can finish a work in 21 days. Christopher can finish the same work in 26 days while Daniel can finish the work in 31 days. How long will it take to finish it if they work together?

(5) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?

(6) If Karen can finish the work in 21 days and Kevin can finish the same work in 24 days, then in how many days both can finish the work together?

(7) 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?

(8) If Myra can finish the work in 15 days and Sophia can finish the same work in 20 days, then in how many days they both can finish the work working together?

(9) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?

(10) If Michelle can finish the work in 44 days and Samuel can finish the same work in 49 days, then in how many days both can finish the work together?