Time and Work
Math MCQs

Question :    If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

Correct Answer  16 ¹⁴/₆₅ days or 16.215 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Sandra = 31 days

And, the number of days to finish the same work by Gary = 34 days

Thus, the number of days to finish the work by Sandra and Gary together = ?

Here,

∵ In 31 days the work done by Sandra = 1

∴ In 1 day, the work done by Sandra = ¹/₃₁ part

Similarly,

∵ In 34 days the work done by Gary = 1

∴ In 1 day, the work done by Gary = ¹/₃₄ part

Now, in 1 day, the work done by Sandra and Gary together

= In 1 day work done by Sandra + In 1 day the work done by Gary

= ¹/₃₁ + ¹/₃₄

= ^{34 + 31}/₁₀₅₄

= ⁶⁵/₁₀₅₄ part of work

This means in 1 day, ⁶⁵/₁₀₅₄ part of work is done by Sandra and Gary working together.

Now, the number of days required to finish ⁶⁵/₁₀₅₄ part of work by Sandra + Gary working together = 1

∴ the number of days required to finish 1 work by Sandra + Gary together

= ¹/_⁶⁵/1054

= 1 × ¹⁰⁵⁴/₆₅ = ¹⁰⁵⁴/₆₅ days

= 16 ¹⁴/₆₅ days = or 16.215 days

Thus, Sandra and Gary working together will finish the work in 16 ¹⁴/₆₅ days = or 16.215 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 Sandra = 31 days

And the number of days required to finish the same work by Gary = 34 days

Thus, the number of days required to finish the work Sandra and Gary working together = ?

Here a = 31 days

And, b = 34 days

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

The number of days required to finish the work when Sandra and Gary working together

= ^{31 × 34}/_{31 + 34} days

= ¹⁰⁵⁴/₆₅ days

= 16 ¹⁴/₆₅ days or 16.215

Thus, Sandra and Gary together will finish the work in 16 ¹⁴/₆₅ days or 16.215 days Answer

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