Time and Work
MCQs Math


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


Similar Questions

(1) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?

(2) Ashley can finish a work in 36 days. Emily can finish the same work in 41 days while Donna can finish the work in 46 days. How long will it take to finish it if they work together?

(3) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(4) 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?

(5) If Thomas can finish the work in 18 days and Andrew can finish the same work in 22 days, then in how many days both can finish the work together?

(6) Susan can finish a work in 18 days. Sarah can finish the same work in 23 days while Karen can finish the work in 28 days. How long will it take to finish it if they work together?

(7) If Dorothy can finish the work in 47 days and Jack can finish the same work in 50 days, then in how many days both can finish the work together?

(8) If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?

(9) If Benjamin can finish the work in 85 days and Gabriel can finish the same work in 90 days, then in how many days both can finish the work together?

(10) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?


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