Time and Work
Math MCQs

Question :    If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?

Correct Answer  49 ⁴³/₁₉₇ days or 49.218 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Carolyn = 96 days

And, the number of days to finish the same work by Ralph = 101 days

Thus, the number of days to finish the work by Carolyn and Ralph together = ?

Here,

∵ In 96 days the work done by Carolyn = 1

∴ In 1 day, the work done by Carolyn = ¹/₉₆ part

Similarly,

∵ In 101 days the work done by Ralph = 1

∴ In 1 day, the work done by Ralph = ¹/₁₀₁ part

Now, in 1 day, the work done by Carolyn and Ralph together

= In 1 day work done by Carolyn + In 1 day the work done by Ralph

= ¹/₉₆ + ¹/₁₀₁

= ^{101 + 96}/₉₆₉₆

= ¹⁹⁷/₉₆₉₆ part of work

This means in 1 day, ¹⁹⁷/₉₆₉₆ part of work is done by Carolyn and Ralph working together.

Now, the number of days required to finish ¹⁹⁷/₉₆₉₆ part of work by Carolyn + Ralph working together = 1

∴ the number of days required to finish 1 work by Carolyn + Ralph together

= ¹/_{¹⁹⁷/9696}

= 1 × ⁹⁶⁹⁶/₁₉₇ = ⁹⁶⁹⁶/₁₉₇ days

= 49 ⁴³/₁₉₇ days = or 49.218 days

Thus, Carolyn and Ralph working together will finish the work in 49 ⁴³/₁₉₇ days = or 49.218 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 Carolyn = 96 days

And the number of days required to finish the same work by Ralph = 101 days

Thus, the number of days required to finish the work Carolyn and Ralph working together = ?

Here a = 96 days

And, b = 101 days

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

The number of days required to finish the work when Carolyn and Ralph working together

= ^{96 × 101}/_{96 + 101} days

= ⁹⁶⁹⁶/₁₉₇ days

= 49 ⁴³/₁₉₇ days or 49.218

Thus, Carolyn and Ralph together will finish the work in 49 ⁴³/₁₉₇ days or 49.218 days Answer

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