Time and Work
Math MCQs

Question :    If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

Correct Answer  37 ¹⁰⁷/₁₅₁ days or 37.709 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jonathan = 73 days

And, the number of days to finish the same work by Sean = 78 days

Thus, the number of days to finish the work by Jonathan and Sean together = ?

Here,

∵ In 73 days the work done by Jonathan = 1

∴ In 1 day, the work done by Jonathan = ¹/₇₃ part

Similarly,

∵ In 78 days the work done by Sean = 1

∴ In 1 day, the work done by Sean = ¹/₇₈ part

Now, in 1 day, the work done by Jonathan and Sean together

= In 1 day work done by Jonathan + In 1 day the work done by Sean

= ¹/₇₃ + ¹/₇₈

= ^{78 + 73}/₅₆₉₄

= ¹⁵¹/₅₆₉₄ part of work

This means in 1 day, ¹⁵¹/₅₆₉₄ part of work is done by Jonathan and Sean working together.

Now, the number of days required to finish ¹⁵¹/₅₆₉₄ part of work by Jonathan + Sean working together = 1

∴ the number of days required to finish 1 work by Jonathan + Sean together

= ¹/_¹⁵¹/5694

= 1 × ⁵⁶⁹⁴/₁₅₁ = ⁵⁶⁹⁴/₁₅₁ days

= 37 ¹⁰⁷/₁₅₁ days = or 37.709 days

Thus, Jonathan and Sean working together will finish the work in 37 ¹⁰⁷/₁₅₁ days = or 37.709 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 Jonathan = 73 days

And the number of days required to finish the same work by Sean = 78 days

Thus, the number of days required to finish the work Jonathan and Sean working together = ?

Here a = 73 days

And, b = 78 days

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

The number of days required to finish the work when Jonathan and Sean working together

= ^{73 × 78}/_{73 + 78} days

= ⁵⁶⁹⁴/₁₅₁ days

= 37 ¹⁰⁷/₁₅₁ days or 37.709

Thus, Jonathan and Sean together will finish the work in 37 ¹⁰⁷/₁₅₁ days or 37.709 days Answer

Similar Questions

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