Time and Work
Math MCQs

Question :    If Joseph can finish the work in 16 days and Steven can finish the same work in 20 days, then in how many days both can finish the work together?

Correct Answer  8 ⁸/₉ days or 8.889 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Joseph = 16 days

And, the number of days to finish the same work by Steven = 20 days

Thus, the number of days to finish the work by Joseph and Steven together = ?

Here,

∵ In 16 days the work done by Joseph = 1

∴ In 1 day, the work done by Joseph = ¹/₁₆ part

Similarly,

∵ In 20 days the work done by Steven = 1

∴ In 1 day, the work done by Steven = ¹/₂₀ part

Now, in 1 day, the work done by Joseph and Steven together

= In 1 day work done by Joseph + In 1 day the work done by Steven

= ¹/₁₆ + ¹/₂₀

= ^{5 + 4}/₈₀

= ⁹/₈₀ part of work

This means in 1 day, ⁹/₈₀ part of work is done by Joseph and Steven working together.

Now, the number of days required to finish ⁹/₈₀ part of work by Joseph + Steven working together = 1

∴ the number of days required to finish 1 work by Joseph + Steven together

= ¹/_⁹/80

= 1 × ⁸⁰/₉ = ⁸⁰/₉ days

= 8 ⁸/₉ days = or 8.889 days

Thus, Joseph and Steven working together will finish the work in 8 ⁸/₉ days = or 8.889 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 Joseph = 16 days

And the number of days required to finish the same work by Steven = 20 days

Thus, the number of days required to finish the work Joseph and Steven working together = ?

Here a = 16 days

And, b = 20 days

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

The number of days required to finish the work when Joseph and Steven working together

= ^{16 × 20}/_{16 + 20} days

= ³²⁰/₃₆ days

= ^{320 ÷ 4}/_{36 ÷ 4} = ⁸⁰/₉ days

= 8 ⁸/₉ days or 8.889

Thus, Joseph and Steven together will finish the work in 8 ⁸/₉ days or 8.889 days Answer

Similar Questions

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(2) Joshua can finish a work in 43 days. Kevin can finish the same work in 48 days while Brian can finish the work in 53 days. How long will it take to finish it if they work together?

(3) If Margaret can finish the work in 29 days and Ryan can finish the same work in 33 days, then in how many days both can finish the work together?

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(6) David can finish a work in 9 days. William can finish the same work in 10 days while Richard can finish the work in 11 days. How long will it take to finish it if they work together?

(7) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

(8) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

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