Time and Work
Math MCQs

Question :    If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

Correct Answer  12 ⁶/₄₉ days or 12.122 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Sarah = 22 days

And, the number of days to finish the same work by Joshua = 27 days

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

Here,

∵ In 22 days the work done by Sarah = 1

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

Similarly,

∵ In 27 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = ¹/₂₇ 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

= ¹/₂₂ + ¹/₂₇

= ^{27 + 22}/₅₉₄

= ⁴⁹/₅₉₄ part of work

This means in 1 day, ⁴⁹/₅₉₄ part of work is done by Sarah and Joshua working together.

Now, the number of days required to finish ⁴⁹/₅₉₄ part of work by Sarah + Joshua working together = 1

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

= ¹/_⁴⁹/594

= 1 × ⁵⁹⁴/₄₉ = ⁵⁹⁴/₄₉ days

= 12 ⁶/₄₉ days = or 12.122 days

Thus, Sarah and Joshua working together will finish the work in 12 ⁶/₄₉ days = or 12.122 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 = 22 days

And the number of days required to finish the same work by Joshua = 27 days

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

Here a = 22 days

And, b = 27 days

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

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

= ^{22 × 27}/_{22 + 27} days

= ⁵⁹⁴/₄₉ days

= 12 ⁶/₄₉ days or 12.122

Thus, Sarah and Joshua together will finish the work in 12 ⁶/₄₉ days or 12.122 days Answer

Similar Questions

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