Time and Work
Math MCQs

Question :    If Susan can finish the work in 15 days and Donald can finish the same work in 18 days, then in how many days both can finish the work together?

Correct Answer  8 ²/₁₁ days or 8.182 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Susan = 15 days

And, the number of days to finish the same work by Donald = 18 days

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

Here,

∵ In 15 days the work done by Susan = 1

∴ In 1 day, the work done by Susan = ¹/₁₅ part

Similarly,

∵ In 18 days the work done by Donald = 1

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

= ¹/₁₅ + ¹/₁₈

= ^{6 + 5}/₉₀

= ¹¹/₉₀ part of work

This means in 1 day, ¹¹/₉₀ part of work is done by Susan and Donald working together.

Now, the number of days required to finish ¹¹/₉₀ part of work by Susan + Donald working together = 1

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

= ¹/_¹¹/90

= 1 × ⁹⁰/₁₁ = ⁹⁰/₁₁ days

= 8 ²/₁₁ days = or 8.182 days

Thus, Susan and Donald working together will finish the work in 8 ²/₁₁ days = or 8.182 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 = 15 days

And the number of days required to finish the same work by Donald = 18 days

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

Here a = 15 days

And, b = 18 days

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

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

= ^{15 × 18}/_{15 + 18} days

= ²⁷⁰/₃₃ days

= ^{270 ÷ 3}/_{33 ÷ 3} = ⁹⁰/₁₁ days

= 8 ²/₁₁ days or 8.182

Thus, Susan and Donald together will finish the work in 8 ²/₁₁ days or 8.182 days Answer

Similar Questions

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(2) Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?

(3) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?

(4) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?

(5) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?

(6) If Dorothy can finish the work in 47 days and Jack can finish the same work in 51 days, then in how many days both can finish the work together?

(7) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?

(8) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?

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