Time and Work
Math MCQs

Question :    If Frank can finish the work in 93 days and Randy can finish the same work in 98 days, then in how many days both can finish the work together?

Correct Answer  47 ¹³⁷/₁₉₁ days or 47.717 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Frank = 93 days

And, the number of days to finish the same work by Randy = 98 days

Thus, the number of days to finish the work by Frank and Randy together = ?

Here,

∵ In 93 days the work done by Frank = 1

∴ In 1 day, the work done by Frank = ¹/₉₃ part

Similarly,

∵ In 98 days the work done by Randy = 1

∴ In 1 day, the work done by Randy = ¹/₉₈ part

Now, in 1 day, the work done by Frank and Randy together

= In 1 day work done by Frank + In 1 day the work done by Randy

= ¹/₉₃ + ¹/₉₈

= ^{98 + 93}/₉₁₁₄

= ¹⁹¹/₉₁₁₄ part of work

This means in 1 day, ¹⁹¹/₉₁₁₄ part of work is done by Frank and Randy working together.

Now, the number of days required to finish ¹⁹¹/₉₁₁₄ part of work by Frank + Randy working together = 1

∴ the number of days required to finish 1 work by Frank + Randy together

= ¹/_¹⁹¹/9114

= 1 × ⁹¹¹⁴/₁₉₁ = ⁹¹¹⁴/₁₉₁ days

= 47 ¹³⁷/₁₉₁ days = or 47.717 days

Thus, Frank and Randy working together will finish the work in 47 ¹³⁷/₁₉₁ days = or 47.717 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 Frank = 93 days

And the number of days required to finish the same work by Randy = 98 days

Thus, the number of days required to finish the work Frank and Randy working together = ?

Here a = 93 days

And, b = 98 days

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

The number of days required to finish the work when Frank and Randy working together

= ^{93 × 98}/_{93 + 98} days

= ⁹¹¹⁴/₁₉₁ days

= 47 ¹³⁷/₁₉₁ days or 47.717

Thus, Frank and Randy together will finish the work in 47 ¹³⁷/₁₉₁ days or 47.717 days Answer

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