Time and Work
Math MCQs

Question :    If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?

Correct Answer  30 ²⁴/₁₂₁ days or 30.198 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Rebecca = 58 days

And, the number of days to finish the same work by Henry = 63 days

Thus, the number of days to finish the work by Rebecca and Henry together = ?

Here,

∵ In 58 days the work done by Rebecca = 1

∴ In 1 day, the work done by Rebecca = ¹/₅₈ part

Similarly,

∵ In 63 days the work done by Henry = 1

∴ In 1 day, the work done by Henry = ¹/₆₃ part

Now, in 1 day, the work done by Rebecca and Henry together

= In 1 day work done by Rebecca + In 1 day the work done by Henry

= ¹/₅₈ + ¹/₆₃

= ^{63 + 58}/₃₆₅₄

= ¹²¹/₃₆₅₄ part of work

This means in 1 day, ¹²¹/₃₆₅₄ part of work is done by Rebecca and Henry working together.

Now, the number of days required to finish ¹²¹/₃₆₅₄ part of work by Rebecca + Henry working together = 1

∴ the number of days required to finish 1 work by Rebecca + Henry together

= ¹/_¹²¹/3654

= 1 × ³⁶⁵⁴/₁₂₁ = ³⁶⁵⁴/₁₂₁ days

= 30 ²⁴/₁₂₁ days = or 30.198 days

Thus, Rebecca and Henry working together will finish the work in 30 ²⁴/₁₂₁ days = or 30.198 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 Rebecca = 58 days

And the number of days required to finish the same work by Henry = 63 days

Thus, the number of days required to finish the work Rebecca and Henry working together = ?

Here a = 58 days

And, b = 63 days

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

The number of days required to finish the work when Rebecca and Henry working together

= ^{58 × 63}/_{58 + 63} days

= ³⁶⁵⁴/₁₂₁ days

= 30 ²⁴/₁₂₁ days or 30.198

Thus, Rebecca and Henry together will finish the work in 30 ²⁴/₁₂₁ days or 30.198 days Answer

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