Time and Work
Math MCQs

Question :    If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?

Correct Answer  31 ¹/₅ days or 31.2 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Sharon = 60 days

And, the number of days to finish the same work by Zachary = 65 days

Thus, the number of days to finish the work by Sharon and Zachary together = ?

Here,

∵ In 60 days the work done by Sharon = 1

∴ In 1 day, the work done by Sharon = ¹/₆₀ part

Similarly,

∵ In 65 days the work done by Zachary = 1

∴ In 1 day, the work done by Zachary = ¹/₆₅ part

Now, in 1 day, the work done by Sharon and Zachary together

= In 1 day work done by Sharon + In 1 day the work done by Zachary

= ¹/₆₀ + ¹/₆₅

= ^{13 + 12}/₇₈₀

= ²⁵/₇₈₀ part of work

= ^{25 ÷ 5}/_{780 ÷ 5} part of work

= ⁵/₁₅₆ part of work

This means, in 1 day, ⁵/₁₅₆ part of the work is done by Sharon and Zachary together.

Now, the number of days required to finish ⁵/₁₅₆ part of work by Sharon + Zachary working together = 1

∴ the number of days required to finish 1 work by Sharon + Zachary together

= ¹/_⁵/156

= 1 × ¹⁵⁶/₅ = ¹⁵⁶/₅ days

= 31 ¹/₅ days = or 31.2 days

Thus, Sharon and Zachary working together will finish the work in 31 ¹/₅ days = or 31.2 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 Sharon = 60 days

And the number of days required to finish the same work by Zachary = 65 days

Thus, the number of days required to finish the work Sharon and Zachary working together = ?

Here a = 60 days

And, b = 65 days

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

The number of days required to finish the work when Sharon and Zachary working together

= ^{60 × 65}/_{60 + 65} days

= ³⁹⁰⁰/₁₂₅ days

= ^{3900 ÷ 25}/_{125 ÷ 25} = ¹⁵⁶/₅ days

= 31 ¹/₅ days or 31.2

Thus, Sharon and Zachary together will finish the work in 31 ¹/₅ days or 31.2 days Answer

Similar Questions

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