Time and Work
Math MCQs

Question :    If Laura can finish the work in 62 days and Kyle can finish the same work in 67 days, then in how many days both can finish the work together?

Correct Answer  32 ²⁶/₁₂₉ days or 32.202 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Laura = 62 days

And, the number of days to finish the same work by Kyle = 67 days

Thus, the number of days to finish the work by Laura and Kyle together = ?

Here,

∵ In 62 days the work done by Laura = 1

∴ In 1 day, the work done by Laura = ¹/₆₂ part

Similarly,

∵ In 67 days the work done by Kyle = 1

∴ In 1 day, the work done by Kyle = ¹/₆₇ part

Now, in 1 day, the work done by Laura and Kyle together

= In 1 day work done by Laura + In 1 day the work done by Kyle

= ¹/₆₂ + ¹/₆₇

= ^{67 + 62}/₄₁₅₄

= ¹²⁹/₄₁₅₄ part of work

This means in 1 day, ¹²⁹/₄₁₅₄ part of work is done by Laura and Kyle working together.

Now, the number of days required to finish ¹²⁹/₄₁₅₄ part of work by Laura + Kyle working together = 1

∴ the number of days required to finish 1 work by Laura + Kyle together

= ¹/_¹²⁹/4154

= 1 × ⁴¹⁵⁴/₁₂₉ = ⁴¹⁵⁴/₁₂₉ days

= 32 ²⁶/₁₂₉ days = or 32.202 days

Thus, Laura and Kyle working together will finish the work in 32 ²⁶/₁₂₉ days = or 32.202 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 Laura = 62 days

And the number of days required to finish the same work by Kyle = 67 days

Thus, the number of days required to finish the work Laura and Kyle working together = ?

Here a = 62 days

And, b = 67 days

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

The number of days required to finish the work when Laura and Kyle working together

= ^{62 × 67}/_{62 + 67} days

= ⁴¹⁵⁴/₁₂₉ days

= 32 ²⁶/₁₂₉ days or 32.202

Thus, Laura and Kyle together will finish the work in 32 ²⁶/₁₂₉ days or 32.202 days Answer

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