Time and Work
Math MCQs

Question :    If George can finish the work in 51 days and Dennis can finish the same work in 56 days, then in how many days both can finish the work together?

Correct Answer  26 ⁷⁴/₁₀₇ days or 26.692 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by George = 51 days

And, the number of days to finish the same work by Dennis = 56 days

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

Here,

∵ In 51 days the work done by George = 1

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

Similarly,

∵ In 56 days the work done by Dennis = 1

∴ In 1 day, the work done by Dennis = ¹/₅₆ 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

= ¹/₅₁ + ¹/₅₆

= ^{56 + 51}/₂₈₅₆

= ¹⁰⁷/₂₈₅₆ part of work

This means in 1 day, ¹⁰⁷/₂₈₅₆ part of work is done by George and Dennis working together.

Now, the number of days required to finish ¹⁰⁷/₂₈₅₆ part of work by George + Dennis working together = 1

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

= ¹/_{¹⁰⁷/2856}

= 1 × ²⁸⁵⁶/₁₀₇ = ²⁸⁵⁶/₁₀₇ days

= 26 ⁷⁴/₁₀₇ days = or 26.692 days

Thus, George and Dennis working together will finish the work in 26 ⁷⁴/₁₀₇ days = or 26.692 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 = 51 days

And the number of days required to finish the same work by Dennis = 56 days

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

Here a = 51 days

And, b = 56 days

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

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

= ^{51 × 56}/_{51 + 56} days

= ²⁸⁵⁶/₁₀₇ days

= 26 ⁷⁴/₁₀₇ days or 26.692

Thus, George and Dennis together will finish the work in 26 ⁷⁴/₁₀₇ days or 26.692 days Answer

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