Time and Work
Math MCQs

Question :    If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

Correct Answer  26 ⁴/₂₁ days or 26.19 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Dorothy = 50 days

And, the number of days to finish the same work by Jack = 55 days

Thus, the number of days to finish the work by Dorothy and Jack together = ?

Here,

∵ In 50 days the work done by Dorothy = 1

∴ In 1 day, the work done by Dorothy = ¹/₅₀ part

Similarly,

∵ In 55 days the work done by Jack = 1

∴ In 1 day, the work done by Jack = ¹/₅₅ part

Now, in 1 day, the work done by Dorothy and Jack together

= In 1 day work done by Dorothy + In 1 day the work done by Jack

= ¹/₅₀ + ¹/₅₅

= ^{11 + 10}/₅₅₀

= ²¹/₅₅₀ part of work

This means in 1 day, ²¹/₅₅₀ part of work is done by Dorothy and Jack working together.

Now, the number of days required to finish ²¹/₅₅₀ part of work by Dorothy + Jack working together = 1

∴ the number of days required to finish 1 work by Dorothy + Jack together

= ¹/_²¹/550

= 1 × ⁵⁵⁰/₂₁ = ⁵⁵⁰/₂₁ days

= 26 ⁴/₂₁ days = or 26.19 days

Thus, Dorothy and Jack working together will finish the work in 26 ⁴/₂₁ days = or 26.19 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 Dorothy = 50 days

And the number of days required to finish the same work by Jack = 55 days

Thus, the number of days required to finish the work Dorothy and Jack working together = ?

Here a = 50 days

And, b = 55 days

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

The number of days required to finish the work when Dorothy and Jack working together

= ^{50 × 55}/_{50 + 55} days

= ²⁷⁵⁰/₁₀₅ days

= ^{2750 ÷ 5}/_{105 ÷ 5} = ⁵⁵⁰/₂₁ days

= 26 ⁴/₂₁ days or 26.19

Thus, Dorothy and Jack together will finish the work in 26 ⁴/₂₁ days or 26.19 days Answer

Similar Questions

(1) If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?

(2) If Pamela can finish the work in 78 days and Dylan can finish the same work in 83 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) If Richard can finish the work in 36 days and Mark can finish the same work in 52 days, then in how many days both can finish the work together?

(5) 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?

(6) 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?

(7) 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?

(8) If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?

(9) If Deborah can finish the work in 54 days and Aaron can finish the same work in 59 days, then in how many days both can finish the work together?

(10) Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?