Question:
If David can finish the work in 32 days and Christopher can finish the same work in 48 days, then in how many days both can finish the work together?
Correct Answer
19 1/5 days or 19.2 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by David = 32 days
And, the number of days to finish the same work by Christopher = 48 days
Thus, the number of days to finish the work by David and Christopher together = ?
Here,
∵ In 32 days the work done by David = 1
∴ In 1 day, the work done by David = 1/32 part
Similarly,
∵ In 48 days the work done by Christopher = 1
∴ In 1 day, the work done by Christopher = 1/48 part
Now, in 1 day, the work done by David and Christopher together
= In 1 day work done by David + In 1 day the work done by Christopher
= 1/32 + 1/48
= 3 + 2/96
= 5/96 part of work
This means in 1 day, 5/96 part of work is done by David and Christopher working together.
Now, the number of days required to finish 5/96 part of work by David + Christopher working together = 1
∴ the number of days required to finish 1 work by David + Christopher together
= 1/5/96
= 1 × 96/5 = 96/5 days
= 19 1/5 days = or 19.2 days
Thus, David and Christopher working together will finish the work in 19 1/5 days = or 19.2 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 David = 32 days
And the number of days required to finish the same work by Christopher = 48 days
Thus, the number of days required to finish the work David and Christopher working together = ?
Here a = 32 days
And, b = 48 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when David and Christopher working together
= 32 × 48/32 + 48 days
= 1536/80 days
= 1536 ÷ 16/80 ÷ 16 = 96/5 days
= 19 1/5 days or 19.2
Thus, David and Christopher together will finish the work in 19 1/5 days or 19.2 days Answer
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