Time and Work
Math MCQs

Question :    If Mark can finish the work in 30 days and Jacob can finish the same work in 33 days, then in how many days both can finish the work together?

Correct Answer  15 ⁵/₇ days or 15.714 days

Solution & Explanation

Solution

Given,

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

And, the number of days to finish the same work by Jacob = 33 days

Thus, the number of days to finish the work by Mark and Jacob together = ?

Here,

∵ In 30 days the work done by Mark = 1

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

Similarly,

∵ In 33 days the work done by Jacob = 1

∴ In 1 day, the work done by Jacob = ¹/₃₃ part

Now, in 1 day, the work done by Mark and Jacob together

= In 1 day work done by Mark + In 1 day the work done by Jacob

= ¹/₃₀ + ¹/₃₃

= ^{11 + 10}/₃₃₀

= ²¹/₃₃₀ part of work

= ^{21 ÷ 3}/_{330 ÷ 3} part of work

= ⁷/₁₁₀ part of work

This means, in 1 day, ⁷/₁₁₀ part of the work is done by Mark and Jacob together.

Now, the number of days required to finish ⁷/₁₁₀ part of work by Mark + Jacob working together = 1

∴ the number of days required to finish 1 work by Mark + Jacob together

= ¹/_⁷/110

= 1 × ¹¹⁰/₇ = ¹¹⁰/₇ days

= 15 ⁵/₇ days = or 15.714 days

Thus, Mark and Jacob working together will finish the work in 15 ⁵/₇ days = or 15.714 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 Mark = 30 days

And the number of days required to finish the same work by Jacob = 33 days

Thus, the number of days required to finish the work Mark and Jacob working together = ?

Here a = 30 days

And, b = 33 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Mark and Jacob working together

= ^{30 × 33}/_{30 + 33} days

= ⁹⁹⁰/₆₃ days

= ^{990 ÷ 9}/_{63 ÷ 9} = ¹¹⁰/₇ days

= 15 ⁵/₇ days or 15.714

Thus, Mark and Jacob together will finish the work in 15 ⁵/₇ days or 15.714 days Answer

Similar Questions

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(2) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?

(3) If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?

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(5) Gary can finish a work in 67 days. Eric can finish the same work in 72 days while Jonathan can finish the work in 77 days. How long will it take to finish it if they work together?

(6) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?

(7) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

(8) Richard can finish a work in 13 days. Joseph can finish the same work in 14 days while Thomas can finish the work in 15 days. How long will it take to finish it if they work together?

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