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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