Time and Work
Math MCQs

Question :    If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 days, then in how many days both can finish the work together?

Correct Answer  10 ¹⁷/₄₂ days or 10.405 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 = 23 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 23 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = ¹/₂₃ 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 + ¹/₂₃

= ^{23 + 19}/₄₃₇

= ⁴²/₄₃₇ part of work

This means in 1 day, ⁴²/₄₃₇ part of work is done by Sarah and Joshua working together.

Now, the number of days required to finish ⁴²/₄₃₇ part of work by Sarah + Joshua working together = 1

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

= ¹/_⁴²/437

= 1 × ⁴³⁷/₄₂ = ⁴³⁷/₄₂ days

= 10 ¹⁷/₄₂ days = or 10.405 days

Thus, Sarah and Joshua working together will finish the work in 10 ¹⁷/₄₂ days = or 10.405 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 = 23 days

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

Here a = 19 days

And, b = 23 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 × 23}/_{19 + 23} days

= ⁴³⁷/₄₂ days

= 10 ¹⁷/₄₂ days or 10.405

Thus, Sarah and Joshua together will finish the work in 10 ¹⁷/₄₂ days or 10.405 days Answer

Similar Questions

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(2) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?

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