Time and Work
Math MCQs

Question :    If Jennifer can finish the work in 7 days and Joseph can finish the same work in 10 days, then in how many days both can finish the work together?

Correct Answer  4 ²/₁₇ days or 4.118 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jennifer = 7 days

And, the number of days to finish the same work by Joseph = 10 days

Thus, the number of days to finish the work by Jennifer and Joseph together = ?

Here,

∵ In 7 days the work done by Jennifer = 1

∴ In 1 day, the work done by Jennifer = ¹/₇ part

Similarly,

∵ In 10 days the work done by Joseph = 1

∴ In 1 day, the work done by Joseph = ¹/₁₀ part

Now, in 1 day, the work done by Jennifer and Joseph together

= In 1 day work done by Jennifer + In 1 day the work done by Joseph

= ¹/₇ + ¹/₁₀

= ^{10 + 7}/₇₀

= ¹⁷/₇₀ part of work

This means in 1 day, ¹⁷/₇₀ part of work is done by Jennifer and Joseph working together.

Now, the number of days required to finish ¹⁷/₇₀ part of work by Jennifer + Joseph working together = 1

∴ the number of days required to finish 1 work by Jennifer + Joseph together

= ¹/_¹⁷/70

= 1 × ⁷⁰/₁₇ = ⁷⁰/₁₇ days

= 4 ²/₁₇ days = or 4.118 days

Thus, Jennifer and Joseph working together will finish the work in 4 ²/₁₇ days = or 4.118 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 Jennifer = 7 days

And the number of days required to finish the same work by Joseph = 10 days

Thus, the number of days required to finish the work Jennifer and Joseph working together = ?

Here a = 7 days

And, b = 10 days

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

The number of days required to finish the work when Jennifer and Joseph working together

= ^{7 × 10}/_{7 + 10} days

= ⁷⁰/₁₇ days

= 4 ²/₁₇ days or 4.118

Thus, Jennifer and Joseph together will finish the work in 4 ²/₁₇ days or 4.118 days Answer

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