Time and Work
Math MCQs

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 & 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 Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

(2) Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?

(3) If Robert can finish the work in 7 days and David can finish the same work in 12 days, then in how many days both can finish the work together?

(4) Kevin can finish a work in 43 days. Brian can finish the same work in 44 days while George can finish the work in 45 days. How long will it take to finish it if they work together?

(5) 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?

(6) If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?

(7) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?

(8) If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?

(9) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?

(10) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?