Time and Work
Math MCQs

Question :    If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?

Correct Answer  23 ⁶⁹/₉₅ days or 23.726 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Brian = 46 days

And, the number of days to finish the same work by Raymond = 49 days

Thus, the number of days to finish the work by Brian and Raymond together = ?

Here,

∵ In 46 days the work done by Brian = 1

∴ In 1 day, the work done by Brian = ¹/₄₆ part

Similarly,

∵ In 49 days the work done by Raymond = 1

∴ In 1 day, the work done by Raymond = ¹/₄₉ part

Now, in 1 day, the work done by Brian and Raymond together

= In 1 day work done by Brian + In 1 day the work done by Raymond

= ¹/₄₆ + ¹/₄₉

= ^{49 + 46}/₂₂₅₄

= ⁹⁵/₂₂₅₄ part of work

This means in 1 day, ⁹⁵/₂₂₅₄ part of work is done by Brian and Raymond working together.

Now, the number of days required to finish ⁹⁵/₂₂₅₄ part of work by Brian + Raymond working together = 1

∴ the number of days required to finish 1 work by Brian + Raymond together

= ¹/_⁹⁵/2254

= 1 × ²²⁵⁴/₉₅ = ²²⁵⁴/₉₅ days

= 23 ⁶⁹/₉₅ days = or 23.726 days

Thus, Brian and Raymond working together will finish the work in 23 ⁶⁹/₉₅ days = or 23.726 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 Brian = 46 days

And the number of days required to finish the same work by Raymond = 49 days

Thus, the number of days required to finish the work Brian and Raymond working together = ?

Here a = 46 days

And, b = 49 days

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

The number of days required to finish the work when Brian and Raymond working together

= ^{46 × 49}/_{46 + 49} days

= ²²⁵⁴/₉₅ days

= 23 ⁶⁹/₉₅ days or 23.726

Thus, Brian and Raymond together will finish the work in 23 ⁶⁹/₉₅ days or 23.726 days Answer

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