Time and Work
Math MCQs

Question :    If Ronald can finish the work in 55 days and Jose can finish the same work in 60 days, then in how many days both can finish the work together?

Correct Answer  28 ¹⁶/₂₃ days or 28.696 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Ronald = 55 days

And, the number of days to finish the same work by Jose = 60 days

Thus, the number of days to finish the work by Ronald and Jose together = ?

Here,

∵ In 55 days the work done by Ronald = 1

∴ In 1 day, the work done by Ronald = ¹/₅₅ part

Similarly,

∵ In 60 days the work done by Jose = 1

∴ In 1 day, the work done by Jose = ¹/₆₀ part

Now, in 1 day, the work done by Ronald and Jose together

= In 1 day work done by Ronald + In 1 day the work done by Jose

= ¹/₅₅ + ¹/₆₀

= ^{12 + 11}/₆₆₀

= ²³/₆₆₀ part of work

This means in 1 day, ²³/₆₆₀ part of work is done by Ronald and Jose working together.

Now, the number of days required to finish ²³/₆₆₀ part of work by Ronald + Jose working together = 1

∴ the number of days required to finish 1 work by Ronald + Jose together

= ¹/_²³/660

= 1 × ⁶⁶⁰/₂₃ = ⁶⁶⁰/₂₃ days

= 28 ¹⁶/₂₃ days = or 28.696 days

Thus, Ronald and Jose working together will finish the work in 28 ¹⁶/₂₃ days = or 28.696 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 Ronald = 55 days

And the number of days required to finish the same work by Jose = 60 days

Thus, the number of days required to finish the work Ronald and Jose working together = ?

Here a = 55 days

And, b = 60 days

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

The number of days required to finish the work when Ronald and Jose working together

= ^{55 × 60}/_{55 + 60} days

= ³³⁰⁰/₁₁₅ days

= ^{3300 ÷ 5}/_{115 ÷ 5} = ⁶⁶⁰/₂₃ days

= 28 ¹⁶/₂₃ days or 28.696

Thus, Ronald and Jose together will finish the work in 28 ¹⁶/₂₃ days or 28.696 days Answer

Similar Questions

(1) 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?

(2) Eric can finish a work in 71 days. Stephen can finish the same work in 76 days while Larry can finish the work in 81 days. How long will it take to finish it if they work together?

(3) Christopher can finish a work in 25 days. Matthew can finish the same work in 30 days while Anthony can finish the work in 35 days. How long will it take to finish it if they work together?

(4) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?

(5) Donald can finish a work in 31 days. Steven can finish the same work in 32 days while Paul can finish the work in 33 days. How long will it take to finish it if they work together?

(6) 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?

(7) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?

(8) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?

(9) If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 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?