Time and Work
MCQs Math


Question:     If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 14 days, then in how many days both can finish the work together?


Correct Answer  6 4/25 days or 6.16 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Elizabeth = 11 days

And, the number of days to finish the same work by Daniel = 14 days

Thus, the number of days to finish the work by Elizabeth and Daniel together = ?

Here,

∵ In 11 days the work done by Elizabeth = 1

∴ In 1 day, the work done by Elizabeth = 1/11 part

Similarly,

∵ In 14 days the work done by Daniel = 1

∴ In 1 day, the work done by Daniel = 1/14 part

Now, in 1 day, the work done by Elizabeth and Daniel together

= In 1 day work done by Elizabeth + In 1 day the work done by Daniel

= 1/11 + 1/14

= 14 + 11/154

= 25/154 part of work

This means in 1 day, 25/154 part of work is done by Elizabeth and Daniel working together.

Now, the number of days required to finish 25/154 part of work by Elizabeth + Daniel working together = 1

∴ the number of days required to finish 1 work by Elizabeth + Daniel together

= 1/25/154

= 1 × 154/25 = 154/25 days

= 6 4/25 days = or 6.16 days

Thus, Elizabeth and Daniel working together will finish the work in 6 4/25 days = or 6.16 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 Elizabeth = 11 days

And the number of days required to finish the same work by Daniel = 14 days

Thus, the number of days required to finish the work Elizabeth and Daniel working together = ?

Here a = 11 days

And, b = 14 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Elizabeth and Daniel working together

= 11 × 14/11 + 14 days

= 154/25 days

= 6 4/25 days or 6.16

Thus, Elizabeth and Daniel together will finish the work in 6 4/25 days or 6.16 days Answer


Similar Questions

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(2) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?

(3) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

(4) 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?

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(6) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?

(7) Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?

(8) If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?

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