Question : If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?
Correct Answer 11 11/12 days or 11.917 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Christopher = 22 days
And, the number of days to finish the same work by Brian = 26 days
Thus, the number of days to finish the work by Christopher and Brian together = ?
Here,
∵ In 22 days the work done by Christopher = 1
∴ In 1 day, the work done by Christopher = 1/22 part
Similarly,
∵ In 26 days the work done by Brian = 1
∴ In 1 day, the work done by Brian = 1/26 part
Now, in 1 day, the work done by Christopher and Brian together
= In 1 day work done by Christopher + In 1 day the work done by Brian
= 1/22 + 1/26
= 13 + 11/286
= 24/286 part of work
= 24 ÷ 2/286 ÷ 2 part of work
= 12/143 part of work
This means, in 1 day, 12/143 part of the work is done by Christopher and Brian together.
Now, the number of days required to finish 12/143 part of work by Christopher + Brian working together = 1
∴ the number of days required to finish 1 work by Christopher + Brian together
= 1/12/143
= 1 × 143/12 = 143/12 days
= 11 11/12 days = or 11.917 days
Thus, Christopher and Brian working together will finish the work in 11 11/12 days = or 11.917 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 Christopher = 22 days
And the number of days required to finish the same work by Brian = 26 days
Thus, the number of days required to finish the work Christopher and Brian working together = ?
Here a = 22 days
And, b = 26 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Christopher and Brian working together
= 22 × 26/22 + 26 days
= 572/48 days
= 572 ÷ 4/48 ÷ 4 = 143/12 days
= 11 11/12 days or 11.917
Thus, Christopher and Brian together will finish the work in 11 11/12 days or 11.917 days Answer
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