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

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