Question : George can finish a work in 51 days. Ronald can finish the same work in 56 days while Edward can finish the work in 61 days. How long will it take to finish it if they work together?
Correct Answer 18 5322/9383 days or 18.567 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by George = 51 days
And, the number of days required to finish the same work by Ronald = 56 days
And, the number of days required to finish the same work by Edward = 61 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 51 days the work is done by George = 1
∴ The work done by George in 1 day = 1/51
Similarly,
∵ In 56 days the work is done by Ronald = 1
∴ The work done by Ronald in 1 day = 1/56
Similarly,
∵ In 61 days the work is done by Edward = 1
∴ The work done by Edward in 1 day = 1/61 part
Now, the work done by George, Ronald, and Edward together in 1 day
= George's 1 day work + Ronald's 1 day work + Edward's 1 day work
= 1/51 + 1/56 + 1/61
= 3416 + 3111 + 2856/174216
= 9383/174216 part of work
This means in 1 day, 9383/174216 part of work is done by George, Ronald and Edward working together.
Now, the number of days required to finish 9383/174216 part of work by George, Ronald, and Edward working together = 1
∴ the number of days required to finish the whole work (1 work) by George + Ronald + Edward together
= 1/9383/174216
= 1 × 174216/9383 = 174216/9383 days
= 18 5322/9383 days = or 18.567 days
Thus, George, Ronald, and Edward working together will finish the total work (1 work) in 18 5322/9383 days = or 18.567 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 George = 51 days
And the number of days required to finish the same work by Ronald = 56 days
And the number of days required to finish the work by Edward = 61 days
Thus, the number of days required to finish the work by George, Ronald, and Edward together = ?
Here a = 51 days
And, b = 56 days
And, c = 61 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when George, Ronald, and Edward working together
= 51 × 56 × 61/51 × 56 + 51 × 61 + 56 × 61 days
= 174216/2856 + 3111 + 3416 days
= 174216/9383 days
= 174216/9383 days
= 18 5322/9383 days or 18.567
Thus, George, Ronald, and Edward together will finish the work in 18 5322/9383 days or 18.567 days Answer
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