Time and Work
Math MCQs

Question :    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?

Correct Answer  9 ⁹/₁₀ days or 9.9 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 = 22 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 22 days the work done by Andrew = 1

∴ In 1 day, the work done by Andrew = ¹/₂₂ 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 + ¹/₂₂

= ^{11 + 9}/₁₉₈

= ²⁰/₁₉₈ part of work

= ^{20 ÷ 2}/_{198 ÷ 2} part of work

= ¹⁰/₉₉ part of work

This means, in 1 day, ¹⁰/₉₉ part of the work is done by Thomas and Andrew together.

Now, the number of days required to finish ¹⁰/₉₉ part of work by Thomas + Andrew working together = 1

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

= ¹/_¹⁰/99

= 1 × ⁹⁹/₁₀ = ⁹⁹/₁₀ days

= 9 ⁹/₁₀ days = or 9.9 days

Thus, Thomas and Andrew working together will finish the work in 9 ⁹/₁₀ days = or 9.9 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 = 22 days

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

Here a = 18 days

And, b = 22 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 × 22}/_{18 + 22} days

= ³⁹⁶/₄₀ days

= ^{396 ÷ 4}/_{40 ÷ 4} = ⁹⁹/₁₀ days

= 9 ⁹/₁₀ days or 9.9

Thus, Thomas and Andrew together will finish the work in 9 ⁹/₁₀ days or 9.9 days Answer

Similar Questions

(1) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?

(2) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?

(3) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?

(4) If Mary can finish the work in 3 days and Michael can finish the same work in 7 days, then in how many days both can finish the work together?

(5) 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?

(6) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?

(7) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?

(8) If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?

(9) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?

(10) Helen can finish a work in 84 days. Katherine can finish the same work in 89 days while Christine can finish the work in 94 days. How long will it take to finish it if they work together?