Time and Work
Math MCQs

Question :    Angela can finish a work in 70 days. Anna can finish the same work in 75 days while Brenda can finish the work in 80 days. How long will it take to finish it if they work together?

Correct Answer  24 ³¹²/₃₃₇ days or 24.926 days

Solution & Explanation

Solution

Given,

The number of days required to finish a piece of work by Angela = 70 days

And, the number of days required to finish the same work by Anna = 75 days

And, the number of days required to finish the same work by Brenda = 80 days

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

Here,

∵ In 70 days the work is done by Angela = 1

∴ The work done by Angela in 1 day = ¹/₇₀

Similarly,

∵ In 75 days the work is done by Anna = 1

∴ The work done by Anna in 1 day = ¹/₇₅

Similarly,

∵ In 80 days the work is done by Brenda = 1

∴ The work done by Brenda in 1 day = ¹/₈₀ part

Now, the work done by Angela, Anna, and Brenda together in 1 day

= Angela's 1 day work + Anna's 1 day work + Brenda's 1 day work

= ¹/₇₀ + ¹/₇₅ + ¹/₈₀

= ^{120 + 112 + 105}/₈₄₀₀

= ³³⁷/₈₄₀₀ part of work

This means in 1 day, ³³⁷/₈₄₀₀ part of work is done by Angela, Anna and Brenda working together.

Now, the number of days required to finish ³³⁷/₈₄₀₀ part of work by Angela, Anna, and Brenda working together = 1

∴ the number of days required to finish the whole work (1 work) by Angela + Anna + Brenda together

= ¹/_³³⁷/8400

= 1 × ⁸⁴⁰⁰/₃₃₇ = ⁸⁴⁰⁰/₃₃₇ days

= 24 ³¹²/₃₃₇ days = or 24.926 days

Thus, Angela, Anna, and Brenda working together will finish the total work (1 work) in 24 ³¹²/₃₃₇ days = or 24.926 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 Angela = 70 days

And the number of days required to finish the same work by Anna = 75 days

And the number of days required to finish the work by Brenda = 80 days

Thus, the number of days required to finish the work by Angela, Anna, and Brenda together = ?

Here a = 70 days

And, b = 75 days

And, c = 80 days

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

The number of days required to finish the work when Angela, Anna, and Brenda working together

= ^{70 × 75 × 80}/_{70 × 75 + 70 × 80 + 75 × 80} days

= ⁴²⁰⁰⁰⁰/_{5250 + 5600 + 6000} days

= ⁴²⁰⁰⁰⁰/₁₆₈₅₀ days

= ⁴²⁰⁰⁰⁰/₁₆₈₅₀ days

= ^{420000 ÷ 50}/_{16850 ÷ 50} = ⁸⁴⁰⁰/₃₃₇ days

= 24 ³¹²/₃₃₇ days or 24.926

Thus, Angela, Anna, and Brenda together will finish the work in 24 ³¹²/₃₃₇ days or 24.926 days Answer

Similar Questions

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(6) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

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