Question : If Catherine can finish the work in 100 days and Mason can finish the same work in 105 days, then in how many days both can finish the work together?
Correct Answer 51 9/41 days or 51.22 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Catherine = 100 days
And, the number of days to finish the same work by Mason = 105 days
Thus, the number of days to finish the work by Catherine and Mason together = ?
Here,
∵ In 100 days the work done by Catherine = 1
∴ In 1 day, the work done by Catherine = 1/100 part
Similarly,
∵ In 105 days the work done by Mason = 1
∴ In 1 day, the work done by Mason = 1/105 part
Now, in 1 day, the work done by Catherine and Mason together
= In 1 day work done by Catherine + In 1 day the work done by Mason
= 1/100 + 1/105
= 21 + 20/2100
= 41/2100 part of work
This means in 1 day, 41/2100 part of work is done by Catherine and Mason working together.
Now, the number of days required to finish 41/2100 part of work by Catherine + Mason working together = 1
∴ the number of days required to finish 1 work by Catherine + Mason together
= 1/41/2100
= 1 × 2100/41 = 2100/41 days
= 51 9/41 days = or 51.22 days
Thus, Catherine and Mason working together will finish the work in 51 9/41 days = or 51.22 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 Catherine = 100 days
And the number of days required to finish the same work by Mason = 105 days
Thus, the number of days required to finish the work Catherine and Mason working together = ?
Here a = 100 days
And, b = 105 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Catherine and Mason working together
= 100 × 105/100 + 105 days
= 10500/205 days
= 10500 ÷ 5/205 ÷ 5 = 2100/41 days
= 51 9/41 days or 51.22
Thus, Catherine and Mason together will finish the work in 51 9/41 days or 51.22 days Answer
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