Time and Work
Math MCQs

Question :    If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?

Correct Answer  8 ²⁴/₃₅ days or 8.686 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Joseph = 16 days

And, the number of days to finish the same work by Steven = 19 days

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

Here,

∵ In 16 days the work done by Joseph = 1

∴ In 1 day, the work done by Joseph = ¹/₁₆ part

Similarly,

∵ In 19 days the work done by Steven = 1

∴ In 1 day, the work done by Steven = ¹/₁₉ part

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

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

= ¹/₁₆ + ¹/₁₉

= ^{19 + 16}/₃₀₄

= ³⁵/₃₀₄ part of work

This means in 1 day, ³⁵/₃₀₄ part of work is done by Joseph and Steven working together.

Now, the number of days required to finish ³⁵/₃₀₄ part of work by Joseph + Steven working together = 1

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

= ¹/_³⁵/304

= 1 × ³⁰⁴/₃₅ = ³⁰⁴/₃₅ days

= 8 ²⁴/₃₅ days = or 8.686 days

Thus, Joseph and Steven working together will finish the work in 8 ²⁴/₃₅ days = or 8.686 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 Joseph = 16 days

And the number of days required to finish the same work by Steven = 19 days

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

Here a = 16 days

And, b = 19 days

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

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

= ^{16 × 19}/_{16 + 19} days

= ³⁰⁴/₃₅ days

= 8 ²⁴/₃₅ days or 8.686

Thus, Joseph and Steven together will finish the work in 8 ²⁴/₃₅ days or 8.686 days Answer

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