Time and Work
MCQs Math


Question:     If George can finish the work in 48 days and Dennis can finish the same work in 51 days, then in how many days both can finish the work together?


Correct Answer  24 8/11 days or 24.727 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by George = 48 days

And, the number of days to finish the same work by Dennis = 51 days

Thus, the number of days to finish the work by George and Dennis together = ?

Here,

∵ In 48 days the work done by George = 1

∴ In 1 day, the work done by George = 1/48 part

Similarly,

∵ In 51 days the work done by Dennis = 1

∴ In 1 day, the work done by Dennis = 1/51 part

Now, in 1 day, the work done by George and Dennis together

= In 1 day work done by George + In 1 day the work done by Dennis

= 1/48 + 1/51

= 17 + 16/816

= 33/816 part of work

= 33 ÷ 3/816 ÷ 3 part of work

= 11/272 part of work

This means, in 1 day, 11/272 part of the work is done by George and Dennis together.

Now, the number of days required to finish 11/272 part of work by George + Dennis working together = 1

∴ the number of days required to finish 1 work by George + Dennis together

= 1/11/272

= 1 × 272/11 = 272/11 days

= 24 8/11 days = or 24.727 days

Thus, George and Dennis working together will finish the work in 24 8/11 days = or 24.727 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 George = 48 days

And the number of days required to finish the same work by Dennis = 51 days

Thus, the number of days required to finish the work George and Dennis working together = ?

Here a = 48 days

And, b = 51 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when George and Dennis working together

= 48 × 51/48 + 51 days

= 2448/99 days

= 2448 ÷ 9/99 ÷ 9 = 272/11 days

= 24 8/11 days or 24.727

Thus, George and Dennis together will finish the work in 24 8/11 days or 24.727 days Answer


Similar Questions

(1) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?

(2) If Justin can finish the work in 79 days and Jesse can finish the same work in 84 days, then in how many days both can finish the work together?

(3) George can finish a work in 51 days. Ronald can finish the same work in 56 days while Edward can finish the work in 61 days. How long will it take to finish it if they work together?

(4) If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?

(5) If Amanda can finish the work in 45 days and Patrick 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 34 days and Jonathan can finish the same work in 37 days, then in how many days both can finish the work together?

(7) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?

(8) Richard can finish a work in 17 days. Thomas can finish the same work in 22 days while Charles can finish the work in 27 days. How long will it take to finish it if they work together?

(9) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

(10) Jonathan can finish a work in 73 days. Larry can finish the same work in 78 days while Justin can finish the work in 83 days. How long will it take to finish it if they work together?


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