Time and Work
Math MCQs

Question :    If Barbara can finish the work in 35 days and Anthony can finish the same work in 51 days, then in how many days both can finish the work together?

Correct Answer  20 ⁶⁵/₈₆ days or 20.756 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Barbara = 35 days

And, the number of days to finish the same work by Anthony = 51 days

Thus, the number of days to finish the work by Barbara and Anthony together = ?

Here,

∵ In 35 days the work done by Barbara = 1

∴ In 1 day, the work done by Barbara = ¹/₃₅ part

Similarly,

∵ In 51 days the work done by Anthony = 1

∴ In 1 day, the work done by Anthony = ¹/₅₁ part

Now, in 1 day, the work done by Barbara and Anthony together

= In 1 day work done by Barbara + In 1 day the work done by Anthony

= ¹/₃₅ + ¹/₅₁

= ^{51 + 35}/₁₇₈₅

= ⁸⁶/₁₇₈₅ part of work

This means in 1 day, ⁸⁶/₁₇₈₅ part of work is done by Barbara and Anthony working together.

Now, the number of days required to finish ⁸⁶/₁₇₈₅ part of work by Barbara + Anthony working together = 1

∴ the number of days required to finish 1 work by Barbara + Anthony together

= ¹/_⁸⁶/1785

= 1 × ¹⁷⁸⁵/₈₆ = ¹⁷⁸⁵/₈₆ days

= 20 ⁶⁵/₈₆ days = or 20.756 days

Thus, Barbara and Anthony working together will finish the work in 20 ⁶⁵/₈₆ days = or 20.756 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 Barbara = 35 days

And the number of days required to finish the same work by Anthony = 51 days

Thus, the number of days required to finish the work Barbara and Anthony working together = ?

Here a = 35 days

And, b = 51 days

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

The number of days required to finish the work when Barbara and Anthony working together

= ^{35 × 51}/_{35 + 51} days

= ¹⁷⁸⁵/₈₆ days

= 20 ⁶⁵/₈₆ days or 20.756

Thus, Barbara and Anthony together will finish the work in 20 ⁶⁵/₈₆ days or 20.756 days Answer

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