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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(2) John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?

(3) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?

(4) Emily can finish a work in 36 days. Donna can finish the same work in 37 days while Michelle can finish the work in 38 days. How long will it take to finish it if they work together?

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(6) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?

(7) If Joshua can finish the work in 43 days and Benjamin can finish the same work in 48 days, then in how many days both can finish the work together?

(8) If Catherine can finish the work in 100 days and Mason can finish the same work in 105 days, then in how many days both can finish the work together?

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