Question : If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?
Correct Answer 37 31/149 days or 37.208 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Shirley = 72 days
And, the number of days to finish the same work by Harold = 77 days
Thus, the number of days to finish the work by Shirley and Harold together = ?
Here,
∵ In 72 days the work done by Shirley = 1
∴ In 1 day, the work done by Shirley = 1/72 part
Similarly,
∵ In 77 days the work done by Harold = 1
∴ In 1 day, the work done by Harold = 1/77 part
Now, in 1 day, the work done by Shirley and Harold together
= In 1 day work done by Shirley + In 1 day the work done by Harold
= 1/72 + 1/77
= 77 + 72/5544
= 149/5544 part of work
This means in 1 day, 149/5544 part of work is done by Shirley and Harold working together.
Now, the number of days required to finish 149/5544 part of work by Shirley + Harold working together = 1
∴ the number of days required to finish 1 work by Shirley + Harold together
= 1/149/5544
= 1 × 5544/149 = 5544/149 days
= 37 31/149 days = or 37.208 days
Thus, Shirley and Harold working together will finish the work in 37 31/149 days = or 37.208 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 Shirley = 72 days
And the number of days required to finish the same work by Harold = 77 days
Thus, the number of days required to finish the work Shirley and Harold working together = ?
Here a = 72 days
And, b = 77 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Shirley and Harold working together
= 72 × 77/72 + 77 days
= 5544/149 days
= 37 31/149 days or 37.208
Thus, Shirley and Harold together will finish the work in 37 31/149 days or 37.208 days Answer
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