Time and Work
MCQs Math


Question:     If David can finish the work in 10 days and Christopher can finish the same work in 14 days, then in how many days both can finish the work together?


Correct Answer  5 5/6 days or 5.833 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by David = 10 days

And, the number of days to finish the same work by Christopher = 14 days

Thus, the number of days to finish the work by David and Christopher together = ?

Here,

∵ In 10 days the work done by David = 1

∴ In 1 day, the work done by David = 1/10 part

Similarly,

∵ In 14 days the work done by Christopher = 1

∴ In 1 day, the work done by Christopher = 1/14 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

= 1/10 + 1/14

= 7 + 5/70

= 12/70 part of work

= 12 ÷ 2/70 ÷ 2 part of work

= 6/35 part of work

This means, in 1 day, 6/35 part of the work is done by David and Christopher together.

Now, the number of days required to finish 6/35 part of work by David + Christopher working together = 1

∴ the number of days required to finish 1 work by David + Christopher together

= 1/6/35

= 1 × 35/6 = 35/6 days

= 5 5/6 days = or 5.833 days

Thus, David and Christopher working together will finish the work in 5 5/6 days = or 5.833 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 = 10 days

And the number of days required to finish the same work by Christopher = 14 days

Thus, the number of days required to finish the work David and Christopher working together = ?

Here a = 10 days

And, b = 14 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when David and Christopher working together

= 10 × 14/10 + 14 days

= 140/24 days

= 140 ÷ 4/24 ÷ 4 = 35/6 days

= 5 5/6 days or 5.833

Thus, David and Christopher together will finish the work in 5 5/6 days or 5.833 days Answer


Similar Questions

(1) Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?

(2) 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?

(3) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?

(4) If Michael can finish the work in 8 days and Thomas can finish the same work in 11 days, then in how many days both can finish the work together?

(5) If Elizabeth can finish the work in 33 days and Daniel can finish the same work in 49 days, then in how many days both can finish the work together?

(6) If Steven can finish the work in 37 days and Jonathan can finish the same work in 42 days, then in how many days both can finish the work together?

(7) If Lisa can finish the work in 26 days and George can finish the same work in 31 days, then in how many days both can finish the work together?

(8) Angela can finish a work in 70 days. Anna can finish the same work in 75 days while Brenda can finish the work in 80 days. How long will it take to finish it if they work together?

(9) If Nancy can finish the work in 25 days and Ronald can finish the same work in 29 days, then in how many days both can finish the work together?

(10) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?


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