Time and Work
Math MCQs

Question :    If Anna can finish the work in 74 days and Austin can finish the same work in 79 days, then in how many days both can finish the work together?

Correct Answer  38 ³²/₁₅₃ days or 38.209 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Anna = 74 days

And, the number of days to finish the same work by Austin = 79 days

Thus, the number of days to finish the work by Anna and Austin together = ?

Here,

∵ In 74 days the work done by Anna = 1

∴ In 1 day, the work done by Anna = ¹/₇₄ part

Similarly,

∵ In 79 days the work done by Austin = 1

∴ In 1 day, the work done by Austin = ¹/₇₉ part

Now, in 1 day, the work done by Anna and Austin together

= In 1 day work done by Anna + In 1 day the work done by Austin

= ¹/₇₄ + ¹/₇₉

= ^{79 + 74}/₅₈₄₆

= ¹⁵³/₅₈₄₆ part of work

This means in 1 day, ¹⁵³/₅₈₄₆ part of work is done by Anna and Austin working together.

Now, the number of days required to finish ¹⁵³/₅₈₄₆ part of work by Anna + Austin working together = 1

∴ the number of days required to finish 1 work by Anna + Austin together

= ¹/_¹⁵³/5846

= 1 × ⁵⁸⁴⁶/₁₅₃ = ⁵⁸⁴⁶/₁₅₃ days

= 38 ³²/₁₅₃ days = or 38.209 days

Thus, Anna and Austin working together will finish the work in 38 ³²/₁₅₃ days = or 38.209 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 Anna = 74 days

And the number of days required to finish the same work by Austin = 79 days

Thus, the number of days required to finish the work Anna and Austin working together = ?

Here a = 74 days

And, b = 79 days

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

The number of days required to finish the work when Anna and Austin working together

= ^{74 × 79}/_{74 + 79} days

= ⁵⁸⁴⁶/₁₅₃ days

= 38 ³²/₁₅₃ days or 38.209

Thus, Anna and Austin together will finish the work in 38 ³²/₁₅₃ days or 38.209 days Answer

Similar Questions

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