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

(1) If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?

(2) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?

(3) If Thomas can finish the work in 18 days and Andrew can finish the same work in 22 days, then in how many days both can finish the work together?

(4) Susan can finish a work in 14 days. Jessica can finish the same work in 15 days while Sarah can finish the work in 16 days. How long will it take to finish it if they work together?

(5) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?

(6) If William can finish the work in 12 days and Matthew can finish the same work in 15 days, then in how many days both can finish the work together?

(7) If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?

(8) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?

(9) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

(10) Robert can finish a work in 7 days. Michael can finish the same work in 12 days while David can finish the work in 17 days. How long will it take to finish it if they work together?