Time and Work
Math MCQs

Question :    If Kevin can finish the work in 47 days and Frank can finish the same work in 52 days, then in how many days both can finish the work together?

Correct Answer  24 ⁶⁸/₉₉ days or 24.687 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kevin = 47 days

And, the number of days to finish the same work by Frank = 52 days

Thus, the number of days to finish the work by Kevin and Frank together = ?

Here,

∵ In 47 days the work done by Kevin = 1

∴ In 1 day, the work done by Kevin = ¹/₄₇ part

Similarly,

∵ In 52 days the work done by Frank = 1

∴ In 1 day, the work done by Frank = ¹/₅₂ part

Now, in 1 day, the work done by Kevin and Frank together

= In 1 day work done by Kevin + In 1 day the work done by Frank

= ¹/₄₇ + ¹/₅₂

= ^{52 + 47}/₂₄₄₄

= ⁹⁹/₂₄₄₄ part of work

This means in 1 day, ⁹⁹/₂₄₄₄ part of work is done by Kevin and Frank working together.

Now, the number of days required to finish ⁹⁹/₂₄₄₄ part of work by Kevin + Frank working together = 1

∴ the number of days required to finish 1 work by Kevin + Frank together

= ¹/_⁹⁹/2444

= 1 × ²⁴⁴⁴/₉₉ = ²⁴⁴⁴/₉₉ days

= 24 ⁶⁸/₉₉ days = or 24.687 days

Thus, Kevin and Frank working together will finish the work in 24 ⁶⁸/₉₉ days = or 24.687 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 Kevin = 47 days

And the number of days required to finish the same work by Frank = 52 days

Thus, the number of days required to finish the work Kevin and Frank working together = ?

Here a = 47 days

And, b = 52 days

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

The number of days required to finish the work when Kevin and Frank working together

= ^{47 × 52}/_{47 + 52} days

= ²⁴⁴⁴/₉₉ days

= 24 ⁶⁸/₉₉ days or 24.687

Thus, Kevin and Frank together will finish the work in 24 ⁶⁸/₉₉ days or 24.687 days Answer

Similar Questions

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