Time and Work
Math MCQs

Question :    If Richard can finish the work in 14 days and Mark can finish the same work in 18 days, then in how many days both can finish the work together?

Correct Answer  7 ⁷/₈ days or 7.875 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Richard = 14 days

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

Thus, the number of days to finish the work by Richard and Mark together = ?

Here,

∵ In 14 days the work done by Richard = 1

∴ In 1 day, the work done by Richard = ¹/₁₄ part

Similarly,

∵ In 18 days the work done by Mark = 1

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

Now, in 1 day, the work done by Richard and Mark together

= In 1 day work done by Richard + In 1 day the work done by Mark

= ¹/₁₄ + ¹/₁₈

= ^{9 + 7}/₁₂₆

= ¹⁶/₁₂₆ part of work

= ^{16 ÷ 2}/_{126 ÷ 2} part of work

= ⁸/₆₃ part of work

This means, in 1 day, ⁸/₆₃ part of the work is done by Richard and Mark together.

Now, the number of days required to finish ⁸/₆₃ part of work by Richard + Mark working together = 1

∴ the number of days required to finish 1 work by Richard + Mark together

= ¹/_⁸/63

= 1 × ⁶³/₈ = ⁶³/₈ days

= 7 ⁷/₈ days = or 7.875 days

Thus, Richard and Mark working together will finish the work in 7 ⁷/₈ days = or 7.875 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 Richard = 14 days

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

Thus, the number of days required to finish the work Richard and Mark working together = ?

Here a = 14 days

And, b = 18 days

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

The number of days required to finish the work when Richard and Mark working together

= ^{14 × 18}/_{14 + 18} days

= ²⁵²/₃₂ days

= ^{252 ÷ 4}/_{32 ÷ 4} = ⁶³/₈ days

= 7 ⁷/₈ days or 7.875

Thus, Richard and Mark together will finish the work in 7 ⁷/₈ days or 7.875 days Answer

Similar Questions

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(2) If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?

(3) Brenda can finish a work in 76 days. Emma can finish the same work in 81 days while Nicole can finish the work in 86 days. How long will it take to finish it if they work together?

(4) If Matthew can finish the work in 29 days and Edward can finish the same work in 34 days, then in how many days both can finish the work together?

(5) Mark can finish a work in 33 days. Steven can finish the same work in 38 days while Paul can finish the work in 43 days. How long will it take to finish it if they work together?

(6) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(7) If Joshua can finish the work in 40 days and Benjamin can finish the same work in 44 days, then in how many days both can finish the work together?

(8) Ashley can finish a work in 36 days. Emily can finish the same work in 41 days while Donna can finish the work in 46 days. How long will it take to finish it if they work together?

(9) Amy can finish a work in 68 days. Shirley can finish the same work in 73 days while Anna can finish the work in 78 days. How long will it take to finish it if they work together?

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