Time and Work
Math MCQs

Question :    If George can finish the work in 48 days and Dennis can finish the same work in 51 days, then in how many days both can finish the work together?

Correct Answer  24 ⁸/₁₁ days or 24.727 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by George = 48 days

And, the number of days to finish the same work by Dennis = 51 days

Thus, the number of days to finish the work by George and Dennis together = ?

Here,

∵ In 48 days the work done by George = 1

∴ In 1 day, the work done by George = ¹/₄₈ part

Similarly,

∵ In 51 days the work done by Dennis = 1

∴ In 1 day, the work done by Dennis = ¹/₅₁ part

Now, in 1 day, the work done by George and Dennis together

= In 1 day work done by George + In 1 day the work done by Dennis

= ¹/₄₈ + ¹/₅₁

= ^{17 + 16}/₈₁₆

= ³³/₈₁₆ part of work

= ^{33 ÷ 3}/_{816 ÷ 3} part of work

= ¹¹/₂₇₂ part of work

This means, in 1 day, ¹¹/₂₇₂ part of the work is done by George and Dennis together.

Now, the number of days required to finish ¹¹/₂₇₂ part of work by George + Dennis working together = 1

∴ the number of days required to finish 1 work by George + Dennis together

= ¹/_¹¹/272

= 1 × ²⁷²/₁₁ = ²⁷²/₁₁ days

= 24 ⁸/₁₁ days = or 24.727 days

Thus, George and Dennis working together will finish the work in 24 ⁸/₁₁ days = or 24.727 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 George = 48 days

And the number of days required to finish the same work by Dennis = 51 days

Thus, the number of days required to finish the work George and Dennis working together = ?

Here a = 48 days

And, b = 51 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when George and Dennis working together

= ^{48 × 51}/_{48 + 51} days

= ²⁴⁴⁸/₉₉ days

= ^{2448 ÷ 9}/_{99 ÷ 9} = ²⁷²/₁₁ days

= 24 ⁸/₁₁ days or 24.727

Thus, George and Dennis together will finish the work in 24 ⁸/₁₁ days or 24.727 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) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?

(3) If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?

(4) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?

(5) 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?

(6) Michelle can finish a work in 40 days. Carol can finish the same work in 41 days while Amanda can finish the work in 42 days. How long will it take to finish it if they work together?

(7) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?

(8) 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?

(9) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?

(10) If Kevin can finish the work in 44 days and Frank can finish the same work in 47 days, then in how many days both can finish the work together?