Time and Work
Math MCQs

Question :    If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?

Correct Answer  35 ¹⁰¹/₁₄₃ days or 35.706 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Nicholas = 69 days

And, the number of days to finish the same work by Roger = 74 days

Thus, the number of days to finish the work by Nicholas and Roger together = ?

Here,

∵ In 69 days the work done by Nicholas = 1

∴ In 1 day, the work done by Nicholas = ¹/₆₉ part

Similarly,

∵ In 74 days the work done by Roger = 1

∴ In 1 day, the work done by Roger = ¹/₇₄ part

Now, in 1 day, the work done by Nicholas and Roger together

= In 1 day work done by Nicholas + In 1 day the work done by Roger

= ¹/₆₉ + ¹/₇₄

= ^{74 + 69}/₅₁₀₆

= ¹⁴³/₅₁₀₆ part of work

This means in 1 day, ¹⁴³/₅₁₀₆ part of work is done by Nicholas and Roger working together.

Now, the number of days required to finish ¹⁴³/₅₁₀₆ part of work by Nicholas + Roger working together = 1

∴ the number of days required to finish 1 work by Nicholas + Roger together

= ¹/_¹⁴³/5106

= 1 × ⁵¹⁰⁶/₁₄₃ = ⁵¹⁰⁶/₁₄₃ days

= 35 ¹⁰¹/₁₄₃ days = or 35.706 days

Thus, Nicholas and Roger working together will finish the work in 35 ¹⁰¹/₁₄₃ days = or 35.706 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 Nicholas = 69 days

And the number of days required to finish the same work by Roger = 74 days

Thus, the number of days required to finish the work Nicholas and Roger working together = ?

Here a = 69 days

And, b = 74 days

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

The number of days required to finish the work when Nicholas and Roger working together

= ^{69 × 74}/_{69 + 74} days

= ⁵¹⁰⁶/₁₄₃ days

= 35 ¹⁰¹/₁₄₃ days or 35.706

Thus, Nicholas and Roger together will finish the work in 35 ¹⁰¹/₁₄₃ days or 35.706 days Answer

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