Time and Work
Math MCQs

Question :    If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?

Correct Answer  42 ¹²²/₁₇₁ days or 42.713 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Brandon = 83 days

And, the number of days to finish the same work by Joe = 88 days

Thus, the number of days to finish the work by Brandon and Joe together = ?

Here,

∵ In 83 days the work done by Brandon = 1

∴ In 1 day, the work done by Brandon = ¹/₈₃ part

Similarly,

∵ In 88 days the work done by Joe = 1

∴ In 1 day, the work done by Joe = ¹/₈₈ part

Now, in 1 day, the work done by Brandon and Joe together

= In 1 day work done by Brandon + In 1 day the work done by Joe

= ¹/₈₃ + ¹/₈₈

= ^{88 + 83}/₇₃₀₄

= ¹⁷¹/₇₃₀₄ part of work

This means in 1 day, ¹⁷¹/₇₃₀₄ part of work is done by Brandon and Joe working together.

Now, the number of days required to finish ¹⁷¹/₇₃₀₄ part of work by Brandon + Joe working together = 1

∴ the number of days required to finish 1 work by Brandon + Joe together

= ¹/_¹⁷¹/7304

= 1 × ⁷³⁰⁴/₁₇₁ = ⁷³⁰⁴/₁₇₁ days

= 42 ¹²²/₁₇₁ days = or 42.713 days

Thus, Brandon and Joe working together will finish the work in 42 ¹²²/₁₇₁ days = or 42.713 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 Brandon = 83 days

And the number of days required to finish the same work by Joe = 88 days

Thus, the number of days required to finish the work Brandon and Joe working together = ?

Here a = 83 days

And, b = 88 days

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

The number of days required to finish the work when Brandon and Joe working together

= ^{83 × 88}/_{83 + 88} days

= ⁷³⁰⁴/₁₇₁ days

= 42 ¹²²/₁₇₁ days or 42.713

Thus, Brandon and Joe together will finish the work in 42 ¹²²/₁₇₁ days or 42.713 days Answer

Similar Questions

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