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 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?

(3) Elizabeth can finish a work in 10 days. Barbara can finish the same work in 11 days while Susan can finish the work in 12 days. How long will it take to finish it if they work together?

(4) If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?

(5) If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?

(6) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

(7) If Linda can finish the work in 31 days and Charles can finish the same work in 47 days, then in how many days both can finish the work together?

(8) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

(9) If Brian can finish the work in 46 days and Raymond can finish the same work in 50 days, then in how many days both can finish the work together?

(10) Gary can finish a work in 67 days. Eric can finish the same work in 72 days while Jonathan can finish the work in 77 days. How long will it take to finish it if they work together?