Question:
If Janet can finish the work in 98 days and Russell can finish the same work in 103 days, then in how many days both can finish the work together?
Correct Answer
50 44/201 days or 50.219 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Janet = 98 days
And, the number of days to finish the same work by Russell = 103 days
Thus, the number of days to finish the work by Janet and Russell together = ?
Here,
∵ In 98 days the work done by Janet = 1
∴ In 1 day, the work done by Janet = 1/98 part
Similarly,
∵ In 103 days the work done by Russell = 1
∴ In 1 day, the work done by Russell = 1/103 part
Now, in 1 day, the work done by Janet and Russell together
= In 1 day work done by Janet + In 1 day the work done by Russell
= 1/98 + 1/103
= 103 + 98/10094
= 201/10094 part of work
This means in 1 day, 201/10094 part of work is done by Janet and Russell working together.
Now, the number of days required to finish 201/10094 part of work by Janet + Russell working together = 1
∴ the number of days required to finish 1 work by Janet + Russell together
= 1/201/10094
= 1 × 10094/201 = 10094/201 days
= 50 44/201 days = or 50.219 days
Thus, Janet and Russell working together will finish the work in 50 44/201 days = or 50.219 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 Janet = 98 days
And the number of days required to finish the same work by Russell = 103 days
Thus, the number of days required to finish the work Janet and Russell working together = ?
Here a = 98 days
And, b = 103 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Janet and Russell working together
= 98 × 103/98 + 103 days
= 10094/201 days
= 50 44/201 days or 50.219
Thus, Janet and Russell together will finish the work in 50 44/201 days or 50.219 days Answer
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