Time and Work
MCQs Math


Question:     If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?


Correct Answer  30 24/121 days or 30.198 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Rebecca = 58 days

And, the number of days to finish the same work by Henry = 63 days

Thus, the number of days to finish the work by Rebecca and Henry together = ?

Here,

∵ In 58 days the work done by Rebecca = 1

∴ In 1 day, the work done by Rebecca = 1/58 part

Similarly,

∵ In 63 days the work done by Henry = 1

∴ In 1 day, the work done by Henry = 1/63 part

Now, in 1 day, the work done by Rebecca and Henry together

= In 1 day work done by Rebecca + In 1 day the work done by Henry

= 1/58 + 1/63

= 63 + 58/3654

= 121/3654 part of work

This means in 1 day, 121/3654 part of work is done by Rebecca and Henry working together.

Now, the number of days required to finish 121/3654 part of work by Rebecca + Henry working together = 1

∴ the number of days required to finish 1 work by Rebecca + Henry together

= 1/121/3654

= 1 × 3654/121 = 3654/121 days

= 30 24/121 days = or 30.198 days

Thus, Rebecca and Henry working together will finish the work in 30 24/121 days = or 30.198 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 Rebecca = 58 days

And the number of days required to finish the same work by Henry = 63 days

Thus, the number of days required to finish the work Rebecca and Henry working together = ?

Here a = 58 days

And, b = 63 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Rebecca and Henry working together

= 58 × 63/58 + 63 days

= 3654/121 days

= 30 24/121 days or 30.198

Thus, Rebecca and Henry together will finish the work in 30 24/121 days or 30.198 days Answer


Similar Questions

(1) Deborah can finish a work in 54 days. Rebecca can finish the same work in 59 days while Sharon can finish the work in 64 days. How long will it take to finish it if they work together?

(2) If Kevin can finish the work in 44 days and Frank can finish the same work in 47 days, then in how many days both can finish the work together?

(3) If Michelle can finish the work in 41 days and Samuel can finish the same work in 45 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 20 days, then in how many days both can finish the work together?

(5) Justin can finish a work in 79 days. Brandon can finish the same work in 84 days while Benjamin can finish the work in 89 days. How long will it take to finish it if they work together?

(6) If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?

(7) Andrew can finish a work in 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?

(8) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?

(9) Rebecca can finish a work in 58 days. Laura can finish the same work in 63 days while Cynthia can finish the work in 68 days. How long will it take to finish it if they work together?

(10) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?


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