Time and Work
Math MCQs

Question :    If Alexander can finish the work in 91 days and Wayne can finish the same work in 96 days, then in how many days both can finish the work together?

Correct Answer  46 ¹³⁴/₁₈₇ days or 46.717 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Alexander = 91 days

And, the number of days to finish the same work by Wayne = 96 days

Thus, the number of days to finish the work by Alexander and Wayne together = ?

Here,

∵ In 91 days the work done by Alexander = 1

∴ In 1 day, the work done by Alexander = ¹/₉₁ part

Similarly,

∵ In 96 days the work done by Wayne = 1

∴ In 1 day, the work done by Wayne = ¹/₉₆ part

Now, in 1 day, the work done by Alexander and Wayne together

= In 1 day work done by Alexander + In 1 day the work done by Wayne

= ¹/₉₁ + ¹/₉₆

= ^{96 + 91}/₈₇₃₆

= ¹⁸⁷/₈₇₃₆ part of work

This means in 1 day, ¹⁸⁷/₈₇₃₆ part of work is done by Alexander and Wayne working together.

Now, the number of days required to finish ¹⁸⁷/₈₇₃₆ part of work by Alexander + Wayne working together = 1

∴ the number of days required to finish 1 work by Alexander + Wayne together

= ¹/_{¹⁸⁷/8736}

= 1 × ⁸⁷³⁶/₁₈₇ = ⁸⁷³⁶/₁₈₇ days

= 46 ¹³⁴/₁₈₇ days = or 46.717 days

Thus, Alexander and Wayne working together will finish the work in 46 ¹³⁴/₁₈₇ days = or 46.717 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 Alexander = 91 days

And the number of days required to finish the same work by Wayne = 96 days

Thus, the number of days required to finish the work Alexander and Wayne working together = ?

Here a = 91 days

And, b = 96 days

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

The number of days required to finish the work when Alexander and Wayne working together

= ^{91 × 96}/_{91 + 96} days

= ⁸⁷³⁶/₁₈₇ days

= 46 ¹³⁴/₁₈₇ days or 46.717

Thus, Alexander and Wayne together will finish the work in 46 ¹³⁴/₁₈₇ days or 46.717 days Answer

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