Time and Work
Math MCQs

Question :    If Jacob can finish the work in 65 days and Noah can finish the same work in 70 days, then in how many days both can finish the work together?

Correct Answer  33 ¹⁹/₂₇ days or 33.704 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jacob = 65 days

And, the number of days to finish the same work by Noah = 70 days

Thus, the number of days to finish the work by Jacob and Noah together = ?

Here,

∵ In 65 days the work done by Jacob = 1

∴ In 1 day, the work done by Jacob = ¹/₆₅ part

Similarly,

∵ In 70 days the work done by Noah = 1

∴ In 1 day, the work done by Noah = ¹/₇₀ part

Now, in 1 day, the work done by Jacob and Noah together

= In 1 day work done by Jacob + In 1 day the work done by Noah

= ¹/₆₅ + ¹/₇₀

= ^{14 + 13}/₉₁₀

= ²⁷/₉₁₀ part of work

This means in 1 day, ²⁷/₉₁₀ part of work is done by Jacob and Noah working together.

Now, the number of days required to finish ²⁷/₉₁₀ part of work by Jacob + Noah working together = 1

∴ the number of days required to finish 1 work by Jacob + Noah together

= ¹/_²⁷/910

= 1 × ⁹¹⁰/₂₇ = ⁹¹⁰/₂₇ days

= 33 ¹⁹/₂₇ days = or 33.704 days

Thus, Jacob and Noah working together will finish the work in 33 ¹⁹/₂₇ days = or 33.704 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 Jacob = 65 days

And the number of days required to finish the same work by Noah = 70 days

Thus, the number of days required to finish the work Jacob and Noah working together = ?

Here a = 65 days

And, b = 70 days

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

The number of days required to finish the work when Jacob and Noah working together

= ^{65 × 70}/_{65 + 70} days

= ⁴⁵⁵⁰/₁₃₅ days

= ^{4550 ÷ 5}/_{135 ÷ 5} = ⁹¹⁰/₂₇ days

= 33 ¹⁹/₂₇ days or 33.704

Thus, Jacob and Noah together will finish the work in 33 ¹⁹/₂₇ days or 33.704 days Answer

Similar Questions

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(2) If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?

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