Time and Work
Math MCQs

Question :    If Jeffrey can finish the work in 61 days and Peter can finish the same work in 66 days, then in how many days both can finish the work together?

Correct Answer  31 ⁸⁹/₁₂₇ days or 31.701 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jeffrey = 61 days

And, the number of days to finish the same work by Peter = 66 days

Thus, the number of days to finish the work by Jeffrey and Peter together = ?

Here,

∵ In 61 days the work done by Jeffrey = 1

∴ In 1 day, the work done by Jeffrey = ¹/₆₁ part

Similarly,

∵ In 66 days the work done by Peter = 1

∴ In 1 day, the work done by Peter = ¹/₆₆ part

Now, in 1 day, the work done by Jeffrey and Peter together

= In 1 day work done by Jeffrey + In 1 day the work done by Peter

= ¹/₆₁ + ¹/₆₆

= ^{66 + 61}/₄₀₂₆

= ¹²⁷/₄₀₂₆ part of work

This means in 1 day, ¹²⁷/₄₀₂₆ part of work is done by Jeffrey and Peter working together.

Now, the number of days required to finish ¹²⁷/₄₀₂₆ part of work by Jeffrey + Peter working together = 1

∴ the number of days required to finish 1 work by Jeffrey + Peter together

= ¹/_¹²⁷/4026

= 1 × ⁴⁰²⁶/₁₂₇ = ⁴⁰²⁶/₁₂₇ days

= 31 ⁸⁹/₁₂₇ days = or 31.701 days

Thus, Jeffrey and Peter working together will finish the work in 31 ⁸⁹/₁₂₇ days = or 31.701 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 Jeffrey = 61 days

And the number of days required to finish the same work by Peter = 66 days

Thus, the number of days required to finish the work Jeffrey and Peter working together = ?

Here a = 61 days

And, b = 66 days

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

The number of days required to finish the work when Jeffrey and Peter working together

= ^{61 × 66}/_{61 + 66} days

= ⁴⁰²⁶/₁₂₇ days

= 31 ⁸⁹/₁₂₇ days or 31.701

Thus, Jeffrey and Peter together will finish the work in 31 ⁸⁹/₁₂₇ days or 31.701 days Answer

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