Time and Work
Math MCQs

Question :    If Benjamin can finish the work in 85 days and Gabriel can finish the same work in 90 days, then in how many days both can finish the work together?

Correct Answer  43 ⁵/₇ days or 43.714 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Benjamin = 85 days

And, the number of days to finish the same work by Gabriel = 90 days

Thus, the number of days to finish the work by Benjamin and Gabriel together = ?

Here,

∵ In 85 days the work done by Benjamin = 1

∴ In 1 day, the work done by Benjamin = ¹/₈₅ part

Similarly,

∵ In 90 days the work done by Gabriel = 1

∴ In 1 day, the work done by Gabriel = ¹/₉₀ part

Now, in 1 day, the work done by Benjamin and Gabriel together

= In 1 day work done by Benjamin + In 1 day the work done by Gabriel

= ¹/₈₅ + ¹/₉₀

= ^{18 + 17}/₁₅₃₀

= ³⁵/₁₅₃₀ part of work

= ^{35 ÷ 5}/_{1530 ÷ 5} part of work

= ⁷/₃₀₆ part of work

This means, in 1 day, ⁷/₃₀₆ part of the work is done by Benjamin and Gabriel together.

Now, the number of days required to finish ⁷/₃₀₆ part of work by Benjamin + Gabriel working together = 1

∴ the number of days required to finish 1 work by Benjamin + Gabriel together

= ¹/_⁷/306

= 1 × ³⁰⁶/₇ = ³⁰⁶/₇ days

= 43 ⁵/₇ days = or 43.714 days

Thus, Benjamin and Gabriel working together will finish the work in 43 ⁵/₇ days = or 43.714 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 Benjamin = 85 days

And the number of days required to finish the same work by Gabriel = 90 days

Thus, the number of days required to finish the work Benjamin and Gabriel working together = ?

Here a = 85 days

And, b = 90 days

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

The number of days required to finish the work when Benjamin and Gabriel working together

= ^{85 × 90}/_{85 + 90} days

= ⁷⁶⁵⁰/₁₇₅ days

= ^{7650 ÷ 25}/_{175 ÷ 25} = ³⁰⁶/₇ days

= 43 ⁵/₇ days or 43.714

Thus, Benjamin and Gabriel together will finish the work in 43 ⁵/₇ days or 43.714 days Answer

Similar Questions

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(2) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?

(3) If Robert can finish the work in 26 days and David can finish the same work in 42 days, then in how many days both can finish the work together?

(4) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?

(5) Jeffrey can finish a work in 61 days. Jacob can finish the same work in 66 days while Gary can finish the work in 71 days. How long will it take to finish it if they work together?

(6) If William can finish the work in 12 days and Matthew can finish the same work in 15 days, then in how many days both can finish the work together?

(7) If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?

(8) If Joshua can finish the work in 43 days and Benjamin can finish the same work in 48 days, then in how many days both can finish the work together?

(9) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?

(10) If Jason can finish the work in 59 days and Douglas can finish the same work in 64 days, then in how many days both can finish the work together?