Time and Work
MCQs Math


Question:     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?


Correct Answer  16 16/17 days or 16.941 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Donald = 32 days

And, the number of days to finish the same work by Nicholas = 36 days

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

Here,

∵ In 32 days the work done by Donald = 1

∴ In 1 day, the work done by Donald = 1/32 part

Similarly,

∵ In 36 days the work done by Nicholas = 1

∴ In 1 day, the work done by Nicholas = 1/36 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

= 1/32 + 1/36

= 9 + 8/288

= 17/288 part of work

This means in 1 day, 17/288 part of work is done by Donald and Nicholas working together.

Now, the number of days required to finish 17/288 part of work by Donald + Nicholas working together = 1

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

= 1/17/288

= 1 × 288/17 = 288/17 days

= 16 16/17 days = or 16.941 days

Thus, Donald and Nicholas working together will finish the work in 16 16/17 days = or 16.941 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 = 32 days

And the number of days required to finish the same work by Nicholas = 36 days

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

Here a = 32 days

And, b = 36 days

Thus, using formula a × b/a + b days

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

= 32 × 36/32 + 36 days

= 1152/68 days

= 1152 ÷ 4/68 ÷ 4 = 288/17 days

= 16 16/17 days or 16.941

Thus, Donald and Nicholas together will finish the work in 16 16/17 days or 16.941 days Answer


Similar Questions

(1) If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?

(2) William can finish a work in 11 days. Richard can finish the same work in 12 days while Joseph can finish the work in 13 days. How long will it take to finish it if they work together?

(3) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

(4) If Amanda can finish the work in 45 days and Patrick can finish the same work in 49 days, then in how many days both can finish the work together?

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(6) If Daniel can finish the work in 27 days and Timothy can finish the same work in 32 days, then in how many days both can finish the work together?

(7) 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?

(8) 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?

(9) Thomas can finish a work in 17 days. Charles can finish the same work in 18 days while Christopher can finish the work in 19 days. How long will it take to finish it if they work together?

(10) If Robert can finish the work in 4 days and David can finish the same work in 7 days, then in how many days both can finish the work together?


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