Time and Work
Math MCQs

Question :    If Steven can finish the work in 34 days and Jonathan can finish the same work in 38 days, then in how many days both can finish the work together?

Correct Answer  17 ¹⁷/₁₈ days or 17.944 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Steven = 34 days

And, the number of days to finish the same work by Jonathan = 38 days

Thus, the number of days to finish the work by Steven and Jonathan together = ?

Here,

∵ In 34 days the work done by Steven = 1

∴ In 1 day, the work done by Steven = ¹/₃₄ part

Similarly,

∵ In 38 days the work done by Jonathan = 1

∴ In 1 day, the work done by Jonathan = ¹/₃₈ part

Now, in 1 day, the work done by Steven and Jonathan together

= In 1 day work done by Steven + In 1 day the work done by Jonathan

= ¹/₃₄ + ¹/₃₈

= ^{19 + 17}/₆₄₆

= ³⁶/₆₄₆ part of work

= ^{36 ÷ 2}/_{646 ÷ 2} part of work

= ¹⁸/₃₂₃ part of work

This means, in 1 day, ¹⁸/₃₂₃ part of the work is done by Steven and Jonathan together.

Now, the number of days required to finish ¹⁸/₃₂₃ part of work by Steven + Jonathan working together = 1

∴ the number of days required to finish 1 work by Steven + Jonathan together

= ¹/_¹⁸/323

= 1 × ³²³/₁₈ = ³²³/₁₈ days

= 17 ¹⁷/₁₈ days = or 17.944 days

Thus, Steven and Jonathan working together will finish the work in 17 ¹⁷/₁₈ days = or 17.944 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 Steven = 34 days

And the number of days required to finish the same work by Jonathan = 38 days

Thus, the number of days required to finish the work Steven and Jonathan working together = ?

Here a = 34 days

And, b = 38 days

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

The number of days required to finish the work when Steven and Jonathan working together

= ^{34 × 38}/_{34 + 38} days

= ¹²⁹²/₇₂ days

= ^{1292 ÷ 4}/_{72 ÷ 4} = ³²³/₁₈ days

= 17 ¹⁷/₁₈ days or 17.944

Thus, Steven and Jonathan together will finish the work in 17 ¹⁷/₁₈ days or 17.944 days Answer

Similar Questions

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(2) If Thomas can finish the work in 18 days and Andrew can finish the same work in 21 days, then in how many days both can finish the work together?

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(6) 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?

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