Time and Work
Math MCQs

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 & 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

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(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) Mary can finish a work in 6 days. Jennifer can finish the same work in 11 days while Linda can finish the work in 16 days. How long will it take to finish it if they work together?

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(5) If Brian can finish the work in 46 days and Raymond can finish the same work in 50 days, then in how many days both can finish the work together?

(6) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?

(7) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?

(8) Benjamin can finish a work in 85 days. Gregory can finish the same work in 90 days while Alexander can finish the work in 95 days. How long will it take to finish it if they work together?

(9) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

(10) 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?