Time and Work
Math MCQs

Question :    If Margaret can finish the work in 29 days and Ryan can finish the same work in 33 days, then in how many days both can finish the work together?

Correct Answer  15 ²⁷/₆₂ days or 15.435 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Margaret = 29 days

And, the number of days to finish the same work by Ryan = 33 days

Thus, the number of days to finish the work by Margaret and Ryan together = ?

Here,

∵ In 29 days the work done by Margaret = 1

∴ In 1 day, the work done by Margaret = ¹/₂₉ part

Similarly,

∵ In 33 days the work done by Ryan = 1

∴ In 1 day, the work done by Ryan = ¹/₃₃ part

Now, in 1 day, the work done by Margaret and Ryan together

= In 1 day work done by Margaret + In 1 day the work done by Ryan

= ¹/₂₉ + ¹/₃₃

= ^{33 + 29}/₉₅₇

= ⁶²/₉₅₇ part of work

This means in 1 day, ⁶²/₉₅₇ part of work is done by Margaret and Ryan working together.

Now, the number of days required to finish ⁶²/₉₅₇ part of work by Margaret + Ryan working together = 1

∴ the number of days required to finish 1 work by Margaret + Ryan together

= ¹/_⁶²/957

= 1 × ⁹⁵⁷/₆₂ = ⁹⁵⁷/₆₂ days

= 15 ²⁷/₆₂ days = or 15.435 days

Thus, Margaret and Ryan working together will finish the work in 15 ²⁷/₆₂ days = or 15.435 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 Margaret = 29 days

And the number of days required to finish the same work by Ryan = 33 days

Thus, the number of days required to finish the work Margaret and Ryan working together = ?

Here a = 29 days

And, b = 33 days

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

The number of days required to finish the work when Margaret and Ryan working together

= ^{29 × 33}/_{29 + 33} days

= ⁹⁵⁷/₆₂ days

= 15 ²⁷/₆₂ days or 15.435

Thus, Margaret and Ryan together will finish the work in 15 ²⁷/₆₂ days or 15.435 days Answer

Similar Questions

(1) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

(2) Richard can finish a work in 13 days. Joseph can finish the same work in 14 days while Thomas can finish the work in 15 days. How long will it take to finish it if they work together?

(3) 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?

(4) If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?

(5) If Donna can finish the work in 42 days and Brandon can finish the same work in 47 days, then in how many days both can finish the work together?

(6) If Donald can finish the work in 32 days and Nicholas can finish the same work in 36 days, then in how many days both can finish the work together?

(7) If Patrick can finish the work in 95 days and Vincent can finish the same work in 100 days, then in how many days both can finish the work together?

(8) If Annie can finish a work in 6 days and Bobby can finish the same work in 12 days, then in how many days they both can finish the work working together?

(9) David can finish a work in 13 days. Richard can finish the same work in 18 days while Joseph can finish the work in 23 days. How long will it take to finish it if they work together?

(10) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?