Question : If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?
Correct Answer 16 48/67 days or 16.716 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Donald = 32 days
And, the number of days to finish the same work by Nicholas = 35 days
Thus, the number of days to finish the work by Donald and Nicholas together = ?
Here,
∵ In 32 days the work done by Donald = 1
∴ In 1 day, the work done by Donald = 1/32 part
Similarly,
∵ In 35 days the work done by Nicholas = 1
∴ In 1 day, the work done by Nicholas = 1/35 part
Now, in 1 day, the work done by Donald and Nicholas together
= In 1 day work done by Donald + In 1 day the work done by Nicholas
= 1/32 + 1/35
= 35 + 32/1120
= 67/1120 part of work
This means in 1 day, 67/1120 part of work is done by Donald and Nicholas working together.
Now, the number of days required to finish 67/1120 part of work by Donald + Nicholas working together = 1
∴ the number of days required to finish 1 work by Donald + Nicholas together
= 1/67/1120
= 1 × 1120/67 = 1120/67 days
= 16 48/67 days = or 16.716 days
Thus, Donald and Nicholas working together will finish the work in 16 48/67 days = or 16.716 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 Donald = 32 days
And the number of days required to finish the same work by Nicholas = 35 days
Thus, the number of days required to finish the work Donald and Nicholas working together = ?
Here a = 32 days
And, b = 35 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Donald and Nicholas working together
= 32 × 35/32 + 35 days
= 1120/67 days
= 16 48/67 days or 16.716
Thus, Donald and Nicholas together will finish the work in 16 48/67 days or 16.716 days Answer
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