Time and Work
MCQs Math


Question:     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?


Correct Answer  16 2/13 days or 16.154 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Betty = 30 days

And, the number of days to finish the same work by Jason = 35 days

Thus, the number of days to finish the work by Betty and Jason together = ?

Here,

∵ In 30 days the work done by Betty = 1

∴ In 1 day, the work done by Betty = 1/30 part

Similarly,

∵ In 35 days the work done by Jason = 1

∴ In 1 day, the work done by Jason = 1/35 part

Now, in 1 day, the work done by Betty and Jason together

= In 1 day work done by Betty + In 1 day the work done by Jason

= 1/30 + 1/35

= 7 + 6/210

= 13/210 part of work

This means in 1 day, 13/210 part of work is done by Betty and Jason working together.

Now, the number of days required to finish 13/210 part of work by Betty + Jason working together = 1

∴ the number of days required to finish 1 work by Betty + Jason together

= 1/13/210

= 1 × 210/13 = 210/13 days

= 16 2/13 days = or 16.154 days

Thus, Betty and Jason working together will finish the work in 16 2/13 days = or 16.154 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 Betty = 30 days

And the number of days required to finish the same work by Jason = 35 days

Thus, the number of days required to finish the work Betty and Jason working together = ?

Here a = 30 days

And, b = 35 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Betty and Jason working together

= 30 × 35/30 + 35 days

= 1050/65 days

= 1050 ÷ 5/65 ÷ 5 = 210/13 days

= 16 2/13 days or 16.154

Thus, Betty and Jason together will finish the work in 16 2/13 days or 16.154 days Answer


Similar Questions

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(2) If Dorothy can finish the work in 47 days and Jack can finish the same work in 51 days, then in how many days both can finish the work together?

(3) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?

(4) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?

(5) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

(6) If Jacob can finish the work in 65 days and Noah can finish the same work in 70 days, then in how many days both can finish the work together?

(7) If Christopher can finish the work in 25 days and Brian can finish the same work in 30 days, then in how many days both can finish the work together?

(8) If William can finish the work in 12 days and Matthew can finish the same work in 16 days, then in how many days both can finish the work together?

(9) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

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