Time and Work
Math MCQs

Question :    If Sarah can finish the work in 19 days and Joshua can finish the same work in 22 days, then in how many days both can finish the work together?

Correct Answer  10 ⁸/₄₁ days or 10.195 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Sarah = 19 days

And, the number of days to finish the same work by Joshua = 22 days

Thus, the number of days to finish the work by Sarah and Joshua together = ?

Here,

∵ In 19 days the work done by Sarah = 1

∴ In 1 day, the work done by Sarah = ¹/₁₉ part

Similarly,

∵ In 22 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = ¹/₂₂ part

Now, in 1 day, the work done by Sarah and Joshua together

= In 1 day work done by Sarah + In 1 day the work done by Joshua

= ¹/₁₉ + ¹/₂₂

= ^{22 + 19}/₄₁₈

= ⁴¹/₄₁₈ part of work

This means in 1 day, ⁴¹/₄₁₈ part of work is done by Sarah and Joshua working together.

Now, the number of days required to finish ⁴¹/₄₁₈ part of work by Sarah + Joshua working together = 1

∴ the number of days required to finish 1 work by Sarah + Joshua together

= ¹/_⁴¹/418

= 1 × ⁴¹⁸/₄₁ = ⁴¹⁸/₄₁ days

= 10 ⁸/₄₁ days = or 10.195 days

Thus, Sarah and Joshua working together will finish the work in 10 ⁸/₄₁ days = or 10.195 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 Sarah = 19 days

And the number of days required to finish the same work by Joshua = 22 days

Thus, the number of days required to finish the work Sarah and Joshua working together = ?

Here a = 19 days

And, b = 22 days

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

The number of days required to finish the work when Sarah and Joshua working together

= ^{19 × 22}/_{19 + 22} days

= ⁴¹⁸/₄₁ days

= 10 ⁸/₄₁ days or 10.195

Thus, Sarah and Joshua together will finish the work in 10 ⁸/₄₁ days or 10.195 days Answer

Similar Questions

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(7) George can finish a work in 47 days. Timothy can finish the same work in 48 days while Ronald can finish the work in 49 days. How long will it take to finish it if they work together?

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