Time and Work
Math MCQs

Question :    If Barbara can finish the work in 13 days and Anthony can finish the same work in 16 days, then in how many days both can finish the work together?

Correct Answer  7 ⁵/₂₉ days or 7.172 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Barbara = 13 days

And, the number of days to finish the same work by Anthony = 16 days

Thus, the number of days to finish the work by Barbara and Anthony together = ?

Here,

∵ In 13 days the work done by Barbara = 1

∴ In 1 day, the work done by Barbara = ¹/₁₃ part

Similarly,

∵ In 16 days the work done by Anthony = 1

∴ In 1 day, the work done by Anthony = ¹/₁₆ part

Now, in 1 day, the work done by Barbara and Anthony together

= In 1 day work done by Barbara + In 1 day the work done by Anthony

= ¹/₁₃ + ¹/₁₆

= ^{16 + 13}/₂₀₈

= ²⁹/₂₀₈ part of work

This means in 1 day, ²⁹/₂₀₈ part of work is done by Barbara and Anthony working together.

Now, the number of days required to finish ²⁹/₂₀₈ part of work by Barbara + Anthony working together = 1

∴ the number of days required to finish 1 work by Barbara + Anthony together

= ¹/_²⁹/208

= 1 × ²⁰⁸/₂₉ = ²⁰⁸/₂₉ days

= 7 ⁵/₂₉ days = or 7.172 days

Thus, Barbara and Anthony working together will finish the work in 7 ⁵/₂₉ days = or 7.172 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 Barbara = 13 days

And the number of days required to finish the same work by Anthony = 16 days

Thus, the number of days required to finish the work Barbara and Anthony working together = ?

Here a = 13 days

And, b = 16 days

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

The number of days required to finish the work when Barbara and Anthony working together

= ^{13 × 16}/_{13 + 16} days

= ²⁰⁸/₂₉ days

= 7 ⁵/₂₉ days or 7.172

Thus, Barbara and Anthony together will finish the work in 7 ⁵/₂₉ days or 7.172 days Answer

Similar Questions

(1) If Barbara can finish the work in 13 days and Anthony can finish the same work in 17 days, then in how many days both can finish the work together?

(2) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?

(3) If Joseph can finish the work in 16 days and Steven can finish the same work in 20 days, then in how many days both can finish the work together?

(4) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(5) If Daniel can finish the work in 27 days and Timothy can finish the same work in 32 days, then in how many days both can finish the work together?

(6) Deborah can finish a work in 50 days. Stephanie can finish the same work in 51 days while Rebecca can finish the work in 52 days. How long will it take to finish it if they work together?

(7) If Sandra can finish the work in 31 days and Gary can finish the same work in 35 days, then in how many days both can finish the work together?

(8) 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?

(9) If Robert can finish a work in 5 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(10) If Elizabeth can finish the work in 14 days and Daniel can finish the same work in 19 days, then in how many days both can finish the work together?