Time and Work
Math MCQs

Question :    If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?

Correct Answer  45 ³⁹/₁₈₁ days or 45.215 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Katherine = 88 days

And, the number of days to finish the same work by Willie = 93 days

Thus, the number of days to finish the work by Katherine and Willie together = ?

Here,

∵ In 88 days the work done by Katherine = 1

∴ In 1 day, the work done by Katherine = ¹/₈₈ part

Similarly,

∵ In 93 days the work done by Willie = 1

∴ In 1 day, the work done by Willie = ¹/₉₃ part

Now, in 1 day, the work done by Katherine and Willie together

= In 1 day work done by Katherine + In 1 day the work done by Willie

= ¹/₈₈ + ¹/₉₃

= ^{93 + 88}/₈₁₈₄

= ¹⁸¹/₈₁₈₄ part of work

This means in 1 day, ¹⁸¹/₈₁₈₄ part of work is done by Katherine and Willie working together.

Now, the number of days required to finish ¹⁸¹/₈₁₈₄ part of work by Katherine + Willie working together = 1

∴ the number of days required to finish 1 work by Katherine + Willie together

= ¹/_¹⁸¹/8184

= 1 × ⁸¹⁸⁴/₁₈₁ = ⁸¹⁸⁴/₁₈₁ days

= 45 ³⁹/₁₈₁ days = or 45.215 days

Thus, Katherine and Willie working together will finish the work in 45 ³⁹/₁₈₁ days = or 45.215 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 Katherine = 88 days

And the number of days required to finish the same work by Willie = 93 days

Thus, the number of days required to finish the work Katherine and Willie working together = ?

Here a = 88 days

And, b = 93 days

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

The number of days required to finish the work when Katherine and Willie working together

= ^{88 × 93}/_{88 + 93} days

= ⁸¹⁸⁴/₁₈₁ days

= 45 ³⁹/₁₈₁ days or 45.215

Thus, Katherine and Willie together will finish the work in 45 ³⁹/₁₈₁ days or 45.215 days Answer

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