Time and Work
Math MCQs

Question :    If Jack can finish the work in 99 days and Bobby can finish the same work in 104 days, then in how many days both can finish the work together?

Correct Answer  50 ¹⁴⁶/₂₀₃ days or 50.719 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jack = 99 days

And, the number of days to finish the same work by Bobby = 104 days

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

Here,

∵ In 99 days the work done by Jack = 1

∴ In 1 day, the work done by Jack = ¹/₉₉ part

Similarly,

∵ In 104 days the work done by Bobby = 1

∴ In 1 day, the work done by Bobby = ¹/₁₀₄ part

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

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

= ¹/₉₉ + ¹/₁₀₄

= ^{104 + 99}/₁₀₂₉₆

= ²⁰³/₁₀₂₉₆ part of work

This means in 1 day, ²⁰³/₁₀₂₉₆ part of work is done by Jack and Bobby working together.

Now, the number of days required to finish ²⁰³/₁₀₂₉₆ part of work by Jack + Bobby working together = 1

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

= ¹/_{²⁰³/10296}

= 1 × ¹⁰²⁹⁶/₂₀₃ = ¹⁰²⁹⁶/₂₀₃ days

= 50 ¹⁴⁶/₂₀₃ days = or 50.719 days

Thus, Jack and Bobby working together will finish the work in 50 ¹⁴⁶/₂₀₃ days = or 50.719 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 Jack = 99 days

And the number of days required to finish the same work by Bobby = 104 days

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

Here a = 99 days

And, b = 104 days

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

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

= ^{99 × 104}/_{99 + 104} days

= ¹⁰²⁹⁶/₂₀₃ days

= 50 ¹⁴⁶/₂₀₃ days or 50.719

Thus, Jack and Bobby together will finish the work in 50 ¹⁴⁶/₂₀₃ days or 50.719 days Answer

Similar Questions

(1) Patricia can finish a work in 4 days. Jennifer can finish the same work in 5 days while Linda can finish the work in 6 days. How long will it take to finish it if they work together?

(2) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

(3) Gary can finish a work in 67 days. Eric can finish the same work in 72 days while Jonathan can finish the work in 77 days. How long will it take to finish it if they work together?

(4) If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?

(5) Karen can finish a work in 24 days. Nancy can finish the same work in 29 days while Betty can finish the work in 34 days. How long will it take to finish it if they work together?

(6) If Jessica can finish the work in 20 days and Paul can finish the same work in 25 days, then in how many days both can finish the work together?

(7) If Ryan can finish the work in 63 days and Ethan can finish the same work in 68 days, then in how many days both can finish the work together?

(8) If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?

(9) 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?

(10) 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?