Time and Work
Math MCQs

Question :    If William can finish the work in 12 days and Matthew can finish the same work in 15 days, then in how many days both can finish the work together?

Correct Answer  6 ²/₃ days or 6.667 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by William = 12 days

And, the number of days to finish the same work by Matthew = 15 days

Thus, the number of days to finish the work by William and Matthew together = ?

Here,

∵ In 12 days the work done by William = 1

∴ In 1 day, the work done by William = ¹/₁₂ part

Similarly,

∵ In 15 days the work done by Matthew = 1

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

Now, in 1 day, the work done by William and Matthew together

= In 1 day work done by William + In 1 day the work done by Matthew

= ¹/₁₂ + ¹/₁₅

= ^{5 + 4}/₆₀

= ⁹/₆₀ part of work

= ^{9 ÷ 3}/_{60 ÷ 3} part of work

= ³/₂₀ part of work

This means, in 1 day, ³/₂₀ part of the work is done by William and Matthew together.

Now, the number of days required to finish ³/₂₀ part of work by William + Matthew working together = 1

∴ the number of days required to finish 1 work by William + Matthew together

= ¹/_³/20

= 1 × ²⁰/₃ = ²⁰/₃ days

= 6 ²/₃ days = or 6.667 days

Thus, William and Matthew working together will finish the work in 6 ²/₃ days = or 6.667 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 William = 12 days

And the number of days required to finish the same work by Matthew = 15 days

Thus, the number of days required to finish the work William and Matthew working together = ?

Here a = 12 days

And, b = 15 days

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

The number of days required to finish the work when William and Matthew working together

= ^{12 × 15}/_{12 + 15} days

= ¹⁸⁰/₂₇ days

= ^{180 ÷ 9}/_{27 ÷ 9} = ²⁰/₃ days

= 6 ²/₃ days or 6.667

Thus, William and Matthew together will finish the work in 6 ²/₃ days or 6.667 days Answer

Similar Questions

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