Time and Work
Math MCQs

Question :    If Thomas can finish the work in 21 days and Andrew can finish the same work in 26 days, then in how many days both can finish the work together?

Correct Answer  11 ²⁹/₄₇ days or 11.617 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Thomas = 21 days

And, the number of days to finish the same work by Andrew = 26 days

Thus, the number of days to finish the work by Thomas and Andrew together = ?

Here,

∵ In 21 days the work done by Thomas = 1

∴ In 1 day, the work done by Thomas = ¹/₂₁ part

Similarly,

∵ In 26 days the work done by Andrew = 1

∴ In 1 day, the work done by Andrew = ¹/₂₆ part

Now, in 1 day, the work done by Thomas and Andrew together

= In 1 day work done by Thomas + In 1 day the work done by Andrew

= ¹/₂₁ + ¹/₂₆

= ^{26 + 21}/₅₄₆

= ⁴⁷/₅₄₆ part of work

This means in 1 day, ⁴⁷/₅₄₆ part of work is done by Thomas and Andrew working together.

Now, the number of days required to finish ⁴⁷/₅₄₆ part of work by Thomas + Andrew working together = 1

∴ the number of days required to finish 1 work by Thomas + Andrew together

= ¹/_⁴⁷/546

= 1 × ⁵⁴⁶/₄₇ = ⁵⁴⁶/₄₇ days

= 11 ²⁹/₄₇ days = or 11.617 days

Thus, Thomas and Andrew working together will finish the work in 11 ²⁹/₄₇ days = or 11.617 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 Thomas = 21 days

And the number of days required to finish the same work by Andrew = 26 days

Thus, the number of days required to finish the work Thomas and Andrew working together = ?

Here a = 21 days

And, b = 26 days

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

The number of days required to finish the work when Thomas and Andrew working together

= ^{21 × 26}/_{21 + 26} days

= ⁵⁴⁶/₄₇ days

= 11 ²⁹/₄₇ days or 11.617

Thus, Thomas and Andrew together will finish the work in 11 ²⁹/₄₇ days or 11.617 days Answer

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