Time and Work
Math MCQs

Question :    If Myra can finish the work in 25 days and Sophia can finish the same work in 15 days, then in how many days they both can finish the work working together?

Correct Answer  9 ³/₈ days or 9.375 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Myra = 25 days

And, the number of days to finish the same work by Sophia = 15 days

Thus, the number of days to finish the work by Myra and Sophia working together = ?

Here, ∵ In 25 days the work done by Myra = 1

∴ In 1 day, the work done by Myra = ¹/₂₅ part

Similarly, ∵ In 15 days the work done by Sophia = 1

∴ In 1 day, the work done by Sophia = ¹/₁₅ part

Now, in 1 day, the work done by Myra and Sophia working together

= In 1 day work done by Myra + In 1 day the work done by Sophia

= ¹/₂₅ + ¹/₁₅

= ^{3 + 5}/₇₅

= ⁸/₇₅ part of work

This means in 1 day, ⁸/₇₅ part of work is done by Myra and Sophia working together.

Now, the number of days required to finish ⁸/₇₅ part of work by Myra + Sophia working together = 1

∴ the number of days required to finish 1 work by Myra + Sophia working together

= ¹/_⁸/75

= 1 × ⁷⁵/₈ = ⁷⁵/₈ days

= 9³/₈ days = 9.375 days

Thus, Myra and Sophia working together will finish the work in 9³/₈ 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 to finish the work by Myra = 25 days

And, the number of days to finish the same work by Sophia = 15 days

Thus, the number of days to finish the work by Myra and Sophia working together = ?

Here "a" = 25 days

And, "b" = 15 days

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

The number of days require to finish the work when Myra and Sophia working together

= ^{25 × 15}/_{25 + 15} days

= ³⁷⁵/₄₀ days

= ^{75 × 5}/_{8 × 5} = ⁷⁵/₈ days

= 9 ³/₈ days or 9.375 days

Thus, Myra and Sophia working together will finish the work in 9 ³/₈ days or 9.375 days Answer

Similar Questions

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(2) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 45 days, then in how many days both can finish the work together?

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(6) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?

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