Time and Work
Math MCQs

Question :    If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?

Correct Answer  6 ⁹/₂₆ days or 6.346 days

Solution & 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 = 15 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 15 days the work done by Daniel = 1

∴ In 1 day, the work done by Daniel = ¹/₁₅ 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 + ¹/₁₅

= ^{15 + 11}/₁₆₅

= ²⁶/₁₆₅ part of work

This means in 1 day, ²⁶/₁₆₅ part of work is done by Elizabeth and Daniel working together.

Now, the number of days required to finish ²⁶/₁₆₅ part of work by Elizabeth + Daniel working together = 1

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

= ¹/_²⁶/165

= 1 × ¹⁶⁵/₂₆ = ¹⁶⁵/₂₆ days

= 6 ⁹/₂₆ days = or 6.346 days

Thus, Elizabeth and Daniel working together will finish the work in 6 ⁹/₂₆ days = or 6.346 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 = 15 days

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

Here a = 11 days

And, b = 15 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 × 15}/_{11 + 15} days

= ¹⁶⁵/₂₆ days

= 6 ⁹/₂₆ days or 6.346

Thus, Elizabeth and Daniel together will finish the work in 6 ⁹/₂₆ days or 6.346 days Answer

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