Time and Work
MCQs Math


Question:     If Donald can finish the work in 35 days and Nicholas can finish the same work in 40 days, then in how many days both can finish the work together?


Correct Answer  18 2/3 days or 18.667 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Donald = 35 days

And, the number of days to finish the same work by Nicholas = 40 days

Thus, the number of days to finish the work by Donald and Nicholas together = ?

Here,

∵ In 35 days the work done by Donald = 1

∴ In 1 day, the work done by Donald = 1/35 part

Similarly,

∵ In 40 days the work done by Nicholas = 1

∴ In 1 day, the work done by Nicholas = 1/40 part

Now, in 1 day, the work done by Donald and Nicholas together

= In 1 day work done by Donald + In 1 day the work done by Nicholas

= 1/35 + 1/40

= 8 + 7/280

= 15/280 part of work

= 15 ÷ 5/280 ÷ 5 part of work

= 3/56 part of work

This means, in 1 day, 3/56 part of the work is done by Donald and Nicholas together.

Now, the number of days required to finish 3/56 part of work by Donald + Nicholas working together = 1

∴ the number of days required to finish 1 work by Donald + Nicholas together

= 1/3/56

= 1 × 56/3 = 56/3 days

= 18 2/3 days = or 18.667 days

Thus, Donald and Nicholas working together will finish the work in 18 2/3 days = or 18.667 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 Donald = 35 days

And the number of days required to finish the same work by Nicholas = 40 days

Thus, the number of days required to finish the work Donald and Nicholas working together = ?

Here a = 35 days

And, b = 40 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Donald and Nicholas working together

= 35 × 40/35 + 40 days

= 1400/75 days

= 1400 ÷ 25/75 ÷ 25 = 56/3 days

= 18 2/3 days or 18.667

Thus, Donald and Nicholas together will finish the work in 18 2/3 days or 18.667 days Answer


Similar Questions

(1) If Michael can finish the work in 8 days and Thomas can finish the same work in 11 days, then in how many days both can finish the work together?

(2) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?

(3) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?

(4) If John can finish the work in 6 days and Richard can finish the same work in 9 days, then in how many days both can finish the work 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 Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?

(7) 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?

(8) If Jessica can finish the work in 17 days and Paul can finish the same work in 20 days, then in how many days both can finish the work together?

(9) Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?

(10) Barbara can finish a work in 12 days. Susan can finish the same work in 13 days while Jessica can finish the work in 14 days. How long will it take to finish it if they work together?


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