Time and Work
Math MCQs

Question :    If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?

Correct Answer  34 ²⁸/₁₃₇ days or 34.204 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kathleen = 66 days

And, the number of days to finish the same work by Jeremy = 71 days

Thus, the number of days to finish the work by Kathleen and Jeremy together = ?

Here,

∵ In 66 days the work done by Kathleen = 1

∴ In 1 day, the work done by Kathleen = ¹/₆₆ part

Similarly,

∵ In 71 days the work done by Jeremy = 1

∴ In 1 day, the work done by Jeremy = ¹/₇₁ part

Now, in 1 day, the work done by Kathleen and Jeremy together

= In 1 day work done by Kathleen + In 1 day the work done by Jeremy

= ¹/₆₆ + ¹/₇₁

= ^{71 + 66}/₄₆₈₆

= ¹³⁷/₄₆₈₆ part of work

This means in 1 day, ¹³⁷/₄₆₈₆ part of work is done by Kathleen and Jeremy working together.

Now, the number of days required to finish ¹³⁷/₄₆₈₆ part of work by Kathleen + Jeremy working together = 1

∴ the number of days required to finish 1 work by Kathleen + Jeremy together

= ¹/_¹³⁷/4686

= 1 × ⁴⁶⁸⁶/₁₃₇ = ⁴⁶⁸⁶/₁₃₇ days

= 34 ²⁸/₁₃₇ days = or 34.204 days

Thus, Kathleen and Jeremy working together will finish the work in 34 ²⁸/₁₃₇ days = or 34.204 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 Kathleen = 66 days

And the number of days required to finish the same work by Jeremy = 71 days

Thus, the number of days required to finish the work Kathleen and Jeremy working together = ?

Here a = 66 days

And, b = 71 days

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

The number of days required to finish the work when Kathleen and Jeremy working together

= ^{66 × 71}/_{66 + 71} days

= ⁴⁶⁸⁶/₁₃₇ days

= 34 ²⁸/₁₃₇ days or 34.204

Thus, Kathleen and Jeremy together will finish the work in 34 ²⁸/₁₃₇ days or 34.204 days Answer

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