Time and Work
Math MCQs

Question :    If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?

Correct Answer  5 ¹/₇ days or 5.143 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 = 12 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 12 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = ¹/₁₂ 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 + ¹/₁₂

= ^{4 + 3}/₃₆

= ⁷/₃₆ part of work

This means in 1 day, ⁷/₃₆ part of work is done by Linda and Charles working together.

Now, the number of days required to finish ⁷/₃₆ part of work by Linda + Charles working together = 1

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

= ¹/_⁷/36

= 1 × ³⁶/₇ = ³⁶/₇ days

= 5 ¹/₇ days = or 5.143 days

Thus, Linda and Charles working together will finish the work in 5 ¹/₇ days = or 5.143 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 = 12 days

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

Here a = 9 days

And, b = 12 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 × 12}/_{9 + 12} days

= ¹⁰⁸/₂₁ days

= ^{108 ÷ 3}/_{21 ÷ 3} = ³⁶/₇ days

= 5 ¹/₇ days or 5.143

Thus, Linda and Charles together will finish the work in 5 ¹/₇ days or 5.143 days Answer

Similar Questions

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