Time and Work
Math MCQs

Question :    If Susan can finish the work in 18 days and Donald can finish the same work in 23 days, then in how many days both can finish the work together?

Correct Answer  10 ⁴/₄₁ days or 10.098 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Susan = 18 days

And, the number of days to finish the same work by Donald = 23 days

Thus, the number of days to finish the work by Susan and Donald together = ?

Here,

∵ In 18 days the work done by Susan = 1

∴ In 1 day, the work done by Susan = ¹/₁₈ part

Similarly,

∵ In 23 days the work done by Donald = 1

∴ In 1 day, the work done by Donald = ¹/₂₃ part

Now, in 1 day, the work done by Susan and Donald together

= In 1 day work done by Susan + In 1 day the work done by Donald

= ¹/₁₈ + ¹/₂₃

= ^{23 + 18}/₄₁₄

= ⁴¹/₄₁₄ part of work

This means in 1 day, ⁴¹/₄₁₄ part of work is done by Susan and Donald working together.

Now, the number of days required to finish ⁴¹/₄₁₄ part of work by Susan + Donald working together = 1

∴ the number of days required to finish 1 work by Susan + Donald together

= ¹/_⁴¹/414

= 1 × ⁴¹⁴/₄₁ = ⁴¹⁴/₄₁ days

= 10 ⁴/₄₁ days = or 10.098 days

Thus, Susan and Donald working together will finish the work in 10 ⁴/₄₁ days = or 10.098 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 Susan = 18 days

And the number of days required to finish the same work by Donald = 23 days

Thus, the number of days required to finish the work Susan and Donald working together = ?

Here a = 18 days

And, b = 23 days

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

The number of days required to finish the work when Susan and Donald working together

= ^{18 × 23}/_{18 + 23} days

= ⁴¹⁴/₄₁ days

= 10 ⁴/₄₁ days or 10.098

Thus, Susan and Donald together will finish the work in 10 ⁴/₄₁ days or 10.098 days Answer

Similar Questions

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(2) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 39 days, then in how many days both can finish the work together?

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(6) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?

(7) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?

(8) If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 days, then in how many days both can finish the work together?

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(10) If George can finish the work in 48 days and Dennis can finish the same work in 52 days, then in how many days both can finish the work together?