Time and Work
Math MCQs

Question :    If Linda can finish the work in 9 days and Charles can finish the same work in 13 days, then in how many days both can finish the work together?

Correct Answer  5 ⁷/₂₂ days or 5.318 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Linda = 9 days

And, the number of days to finish the same work by Charles = 13 days

Thus, the number of days to finish the work by Linda and Charles together = ?

Here,

∵ In 9 days the work done by Linda = 1

∴ In 1 day, the work done by Linda = ¹/₉ part

Similarly,

∵ In 13 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = ¹/₁₃ part

Now, in 1 day, the work done by Linda and Charles together

= In 1 day work done by Linda + In 1 day the work done by Charles

= ¹/₉ + ¹/₁₃

= ^{13 + 9}/₁₁₇

= ²²/₁₁₇ part of work

This means in 1 day, ²²/₁₁₇ part of work is done by Linda and Charles working together.

Now, the number of days required to finish ²²/₁₁₇ part of work by Linda + Charles working together = 1

∴ the number of days required to finish 1 work by Linda + Charles together

= ¹/_²²/117

= 1 × ¹¹⁷/₂₂ = ¹¹⁷/₂₂ days

= 5 ⁷/₂₂ days = or 5.318 days

Thus, Linda and Charles working together will finish the work in 5 ⁷/₂₂ days = or 5.318 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 Linda = 9 days

And the number of days required to finish the same work by Charles = 13 days

Thus, the number of days required to finish the work Linda and Charles working together = ?

Here a = 9 days

And, b = 13 days

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

The number of days required to finish the work when Linda and Charles working together

= ^{9 × 13}/_{9 + 13} days

= ¹¹⁷/₂₂ days

= 5 ⁷/₂₂ days or 5.318

Thus, Linda and Charles together will finish the work in 5 ⁷/₂₂ days or 5.318 days Answer

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