Time and Work
Math MCQs

Question :    Rebecca can finish a work in 58 days. Laura can finish the same work in 63 days while Cynthia can finish the work in 68 days. How long will it take to finish it if they work together?

Correct Answer  20 ⁵⁴¹⁶/₅₉₄₁ days or 20.912 days

Solution & Explanation

Solution

Given,

The number of days required to finish a piece of work by Rebecca = 58 days

And, the number of days required to finish the same work by Laura = 63 days

And, the number of days required to finish the same work by Cynthia = 68 days

Thus, the number of days required to finish the work by all of them if they work together = ?

Here,

∵ In 58 days the work is done by Rebecca = 1

∴ The work done by Rebecca in 1 day = ¹/₅₈

Similarly,

∵ In 63 days the work is done by Laura = 1

∴ The work done by Laura in 1 day = ¹/₆₃

Similarly,

∵ In 68 days the work is done by Cynthia = 1

∴ The work done by Cynthia in 1 day = ¹/₆₈ part

Now, the work done by Rebecca, Laura, and Cynthia together in 1 day

= Rebecca's 1 day work + Laura's 1 day work + Cynthia's 1 day work

= ¹/₅₈ + ¹/₆₃ + ¹/₆₈

= ^{2142 + 1972 + 1827}/₁₂₄₂₃₆

= ⁵⁹⁴¹/₁₂₄₂₃₆ part of work

This means in 1 day, ⁵⁹⁴¹/₁₂₄₂₃₆ part of work is done by Rebecca, Laura and Cynthia working together.

Now, the number of days required to finish ⁵⁹⁴¹/₁₂₄₂₃₆ part of work by Rebecca, Laura, and Cynthia working together = 1

∴ the number of days required to finish the whole work (1 work) by Rebecca + Laura + Cynthia together

= ¹/_{⁵⁹⁴¹/124236}

= 1 × ¹²⁴²³⁶/₅₉₄₁ = ¹²⁴²³⁶/₅₉₄₁ days

= 20 ⁵⁴¹⁶/₅₉₄₁ days = or 20.912 days

Thus, Rebecca, Laura, and Cynthia working together will finish the total work (1 work) in 20 ⁵⁴¹⁶/₅₉₄₁ days = or 20.912 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= ^{a × b × c}/_{ab + ac + bc} days.

Here given,

The number of days required to finish the work by Rebecca = 58 days

And the number of days required to finish the same work by Laura = 63 days

And the number of days required to finish the work by Cynthia = 68 days

Thus, the number of days required to finish the work by Rebecca, Laura, and Cynthia together = ?

Here a = 58 days

And, b = 63 days

And, c = 68 days

Thus, using formula ^{a × b × c}/_{ab + ac + bc} days

The number of days required to finish the work when Rebecca, Laura, and Cynthia working together

= ^{58 × 63 × 68}/_{58 × 63 + 58 × 68 + 63 × 68} days

= ²⁴⁸⁴⁷²/_{3654 + 3944 + 4284} days

= ²⁴⁸⁴⁷²/₁₁₈₈₂ days

= ²⁴⁸⁴⁷²/₁₁₈₈₂ days

= ^{248472 ÷ 2}/_{11882 ÷ 2} = ¹²⁴²³⁶/₅₉₄₁ days

= 20 ⁵⁴¹⁶/₅₉₄₁ days or 20.912

Thus, Rebecca, Laura, and Cynthia together will finish the work in 20 ⁵⁴¹⁶/₅₉₄₁ days or 20.912 days Answer

Similar Questions

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