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 William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?

(2) If Timothy can finish the work in 53 days and Tyler can finish the same work in 58 days, then in how many days both can finish the work together?

(3) If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?

(4) If Richard can finish the work in 14 days and Mark can finish the same work in 18 days, then in how many days both can finish the work together?

(5) William can finish a work in 15 days. Joseph can finish the same work in 20 days while Thomas can finish the work in 25 days. How long will it take to finish it if they work together?

(6) Steven can finish a work in 33 days. Paul can finish the same work in 34 days while Andrew can finish the work in 35 days. How long will it take to finish it if they work together?

(7) If Karen can finish the work in 21 days and Kevin can finish the same work in 25 days, then in how many days both can finish the work together?

(8) If Andrew can finish the work in 38 days and Scott can finish the same work in 41 days, then in how many days both can finish the work together?

(9) Joshua can finish a work in 39 days. Kenneth can finish the same work in 40 days while Kevin can finish the work in 41 days. How long will it take to finish it if they work together?

(10) Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©