🏡 Home
    1. Time and Distance
    2. Time and Work
    3. Profit And Loss
    4. Average
    5. Percentage
    6. Simple Interest
    7. Questions based on ages
    1. Math
    2. Chemistry
    3. Chemistry Hindi
    4. Biology
    5. Exemplar Solution
    1. 11th physics
    2. 11th physics-hindi
    1. Science 10th (English)
    2. Science 10th (Hindi)
    3. Mathematics
    4. Math (Hindi)
    5. Social Science
    1. Science (English)
    2. 9th-Science (Hindi)
    1. 8th-Science (English)
    2. 8th-Science (Hindi)
    3. 8th-math (English)
    4. 8th-math (Hindi)
    1. 7th Math
    2. 7th Math(Hindi)
    1. Sixth Science
    2. 6th Science(hindi)
    1. Five Science
    1. Science (English)
    2. Science (Hindi)
    1. Std 10 science
    2. Std 4 science
    3. Std two EVS
    4. Std two Math
    5. MCQs Math
    6. एमoसीoक्यूo गणित
    7. Civil Service
    1. General Math (Hindi version)
    1. About Us
    2. Contact Us
10upon10.com

Time and Work
Math MCQs


Question :    Brandon can finish a work in 83 days. Samuel can finish the same work in 88 days while Gregory can finish the work in 93 days. How long will it take to finish it if they work together?


Correct Answer  29 6269/23207 days or 29.27 days

Solution & Explanation

Solution

Given,

The number of days required to finish a piece of work by Brandon = 83 days

And, the number of days required to finish the same work by Samuel = 88 days

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

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

Here,

∵ In 83 days the work is done by Brandon = 1

∴ The work done by Brandon in 1 day = 1/83

Similarly,

∵ In 88 days the work is done by Samuel = 1

∴ The work done by Samuel in 1 day = 1/88

Similarly,

∵ In 93 days the work is done by Gregory = 1

∴ The work done by Gregory in 1 day = 1/93 part

Now, the work done by Brandon, Samuel, and Gregory together in 1 day

= Brandon's 1 day work + Samuel's 1 day work + Gregory's 1 day work

= 1/83 + 1/88 + 1/93

= 8184 + 7719 + 7304/679272

= 23207/679272 part of work

This means in 1 day, 23207/679272 part of work is done by Brandon, Samuel and Gregory working together.

Now, the number of days required to finish 23207/679272 part of work by Brandon, Samuel, and Gregory working together = 1

∴ the number of days required to finish the whole work (1 work) by Brandon + Samuel + Gregory together

= 1/23207/679272

= 1 × 679272/23207 = 679272/23207 days

= 29 6269/23207 days = or 29.27 days

Thus, Brandon, Samuel, and Gregory working together will finish the total work (1 work) in 29 6269/23207 days = or 29.27 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 Brandon = 83 days

And the number of days required to finish the same work by Samuel = 88 days

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

Thus, the number of days required to finish the work by Brandon, Samuel, and Gregory together = ?

Here a = 83 days

And, b = 88 days

And, c = 93 days

Thus, using formula a × b × c/ab + ac + bc days

The number of days required to finish the work when Brandon, Samuel, and Gregory working together

= 83 × 88 × 93/83 × 88 + 83 × 93 + 88 × 93 days

= 679272/7304 + 7719 + 8184 days

= 679272/23207 days

= 679272/23207 days

= 29 6269/23207 days or 29.27

Thus, Brandon, Samuel, and Gregory together will finish the work in 29 6269/23207 days or 29.27 days Answer


Similar Questions

(1) If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?

(2) Brenda can finish a work in 76 days. Emma can finish the same work in 81 days while Nicole can finish the work in 86 days. How long will it take to finish it if they work together?

(3) If Brian can finish the work in 49 days and Raymond can finish the same work in 54 days, then in how many days both can finish the work together?

(4) If Betty can finish the work in 27 days and Jason can finish the same work in 31 days, then in how many days both can finish the work together?

(5) Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?

(6) If Pamela can finish the work in 78 days and Dylan can finish the same work in 83 days, then in how many days both can finish the work together?

(7) If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?

(8) Sharon can finish a work in 60 days. Cynthia can finish the same work in 65 days while Kathleen can finish the work in 70 days. How long will it take to finish it if they work together?

(9) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?

(10) Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?