Time and Work
MCQs Math


Question:     If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?


Correct Answer  37 31/149 days or 37.208 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Shirley = 72 days

And, the number of days to finish the same work by Harold = 77 days

Thus, the number of days to finish the work by Shirley and Harold together = ?

Here,

∵ In 72 days the work done by Shirley = 1

∴ In 1 day, the work done by Shirley = 1/72 part

Similarly,

∵ In 77 days the work done by Harold = 1

∴ In 1 day, the work done by Harold = 1/77 part

Now, in 1 day, the work done by Shirley and Harold together

= In 1 day work done by Shirley + In 1 day the work done by Harold

= 1/72 + 1/77

= 77 + 72/5544

= 149/5544 part of work

This means in 1 day, 149/5544 part of work is done by Shirley and Harold working together.

Now, the number of days required to finish 149/5544 part of work by Shirley + Harold working together = 1

∴ the number of days required to finish 1 work by Shirley + Harold together

= 1/149/5544

= 1 × 5544/149 = 5544/149 days

= 37 31/149 days = or 37.208 days

Thus, Shirley and Harold working together will finish the work in 37 31/149 days = or 37.208 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 Shirley = 72 days

And the number of days required to finish the same work by Harold = 77 days

Thus, the number of days required to finish the work Shirley and Harold working together = ?

Here a = 72 days

And, b = 77 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Shirley and Harold working together

= 72 × 77/72 + 77 days

= 5544/149 days

= 37 31/149 days or 37.208

Thus, Shirley and Harold together will finish the work in 37 31/149 days or 37.208 days Answer


Similar Questions

(1) Daniel can finish a work in 27 days. Anthony can finish the same work in 32 days while Mark can finish the work in 37 days. How long will it take to finish it if they work together?

(2) Linda can finish a work in 12 days. Barbara can finish the same work in 17 days while Susan can finish the work in 22 days. How long will it take to finish it if they work together?

(3) 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?

(4) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(5) If Richard can finish the work in 17 days and Mark can finish the same work in 22 days, then in how many days both can finish the work together?

(6) 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?

(7) Joshua can finish a work in 39 days. Kenneth can finish the same work in 40 days while Kevin can finish the work in 41 days. How long will it take to finish it if they work together?

(8) 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?

(9) Dorothy can finish a work in 46 days. Melissa can finish the same work in 47 days while Deborah can finish the work in 48 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 36 days, then in how many days both can finish the work together?


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