Time and Work
MCQs Math


Question:     If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?


Correct Answer  21 3/17 days or 21.176 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Emily = 40 days

And, the number of days to finish the same work by Justin = 45 days

Thus, the number of days to finish the work by Emily and Justin together = ?

Here,

∵ In 40 days the work done by Emily = 1

∴ In 1 day, the work done by Emily = 1/40 part

Similarly,

∵ In 45 days the work done by Justin = 1

∴ In 1 day, the work done by Justin = 1/45 part

Now, in 1 day, the work done by Emily and Justin together

= In 1 day work done by Emily + In 1 day the work done by Justin

= 1/40 + 1/45

= 9 + 8/360

= 17/360 part of work

This means in 1 day, 17/360 part of work is done by Emily and Justin working together.

Now, the number of days required to finish 17/360 part of work by Emily + Justin working together = 1

∴ the number of days required to finish 1 work by Emily + Justin together

= 1/17/360

= 1 × 360/17 = 360/17 days

= 21 3/17 days = or 21.176 days

Thus, Emily and Justin working together will finish the work in 21 3/17 days = or 21.176 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 Emily = 40 days

And the number of days required to finish the same work by Justin = 45 days

Thus, the number of days required to finish the work Emily and Justin working together = ?

Here a = 40 days

And, b = 45 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Emily and Justin working together

= 40 × 45/40 + 45 days

= 1800/85 days

= 1800 ÷ 5/85 ÷ 5 = 360/17 days

= 21 3/17 days or 21.176

Thus, Emily and Justin together will finish the work in 21 3/17 days or 21.176 days Answer


Similar Questions

(1) Anthony can finish a work in 31 days. Donald can finish the same work in 36 days while Steven can finish the work in 41 days. How long will it take to finish it if they work together?

(2) Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?

(3) If Karen can finish the work in 21 days and Kevin can finish the same work in 25 days, then in how many days both can finish the work together?

(4) If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?

(5) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

(6) If Nicole can finish the work in 82 days and Billy can finish the same work in 87 days, then in how many days both can finish the work together?

(7) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?

(8) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 39 days, then in how many days both can finish the work together?

(9) If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?

(10) If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?


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