Time and Work
Math MCQs

Question :    If Richard can finish the work in 36 days and Mark can finish the same work in 52 days, then in how many days both can finish the work together?

Correct Answer  21 ³/₁₁ days or 21.273 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Richard = 36 days

And, the number of days to finish the same work by Mark = 52 days

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

Here,

∵ In 36 days the work done by Richard = 1

∴ In 1 day, the work done by Richard = ¹/₃₆ part

Similarly,

∵ In 52 days the work done by Mark = 1

∴ In 1 day, the work done by Mark = ¹/₅₂ 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

= ¹/₃₆ + ¹/₅₂

= ^{13 + 9}/₄₆₈

= ²²/₄₆₈ part of work

= ^{22 ÷ 2}/_{468 ÷ 2} part of work

= ¹¹/₂₃₄ part of work

This means, in 1 day, ¹¹/₂₃₄ part of the work is done by Richard and Mark together.

Now, the number of days required to finish ¹¹/₂₃₄ part of work by Richard + Mark working together = 1

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

= ¹/_¹¹/234

= 1 × ²³⁴/₁₁ = ²³⁴/₁₁ days

= 21 ³/₁₁ days = or 21.273 days

Thus, Richard and Mark working together will finish the work in 21 ³/₁₁ days = or 21.273 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 = 36 days

And the number of days required to finish the same work by Mark = 52 days

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

Here a = 36 days

And, b = 52 days

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

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

= ^{36 × 52}/_{36 + 52} days

= ¹⁸⁷²/₈₈ days

= ^{1872 ÷ 8}/_{88 ÷ 8} = ²³⁴/₁₁ days

= 21 ³/₁₁ days or 21.273

Thus, Richard and Mark together will finish the work in 21 ³/₁₁ days or 21.273 days Answer

Similar Questions

(1) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(2) Joseph can finish a work in 19 days. Charles can finish the same work in 24 days while Christopher can finish the work in 29 days. How long will it take to finish it if they work together?

(3) If Mark can finish the work in 30 days and Jacob can finish the same work in 33 days, then in how many days both can finish the work together?

(4) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

(5) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?

(6) If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?

(7) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

(8) John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?

(9) 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?

(10) If Lisa can finish the work in 26 days and George can finish the same work in 31 days, then in how many days both can finish the work together?