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

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(2) Timothy can finish a work in 49 days. Ronald can finish the same work in 50 days while Edward can finish the work in 51 days. How long will it take to finish it if they work together?

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(6) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

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(9) 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?

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