Time and Work
Math MCQs

Question :    If Linda can finish the work in 31 days and Charles can finish the same work in 47 days, then in how many days both can finish the work together?

Correct Answer  18 ⁵³/₇₈ days or 18.679 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Linda = 31 days

And, the number of days to finish the same work by Charles = 47 days

Thus, the number of days to finish the work by Linda and Charles together = ?

Here,

∵ In 31 days the work done by Linda = 1

∴ In 1 day, the work done by Linda = ¹/₃₁ part

Similarly,

∵ In 47 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = ¹/₄₇ part

Now, in 1 day, the work done by Linda and Charles together

= In 1 day work done by Linda + In 1 day the work done by Charles

= ¹/₃₁ + ¹/₄₇

= ^{47 + 31}/₁₄₅₇

= ⁷⁸/₁₄₅₇ part of work

This means in 1 day, ⁷⁸/₁₄₅₇ part of work is done by Linda and Charles working together.

Now, the number of days required to finish ⁷⁸/₁₄₅₇ part of work by Linda + Charles working together = 1

∴ the number of days required to finish 1 work by Linda + Charles together

= ¹/_⁷⁸/1457

= 1 × ¹⁴⁵⁷/₇₈ = ¹⁴⁵⁷/₇₈ days

= 18 ⁵³/₇₈ days = or 18.679 days

Thus, Linda and Charles working together will finish the work in 18 ⁵³/₇₈ days = or 18.679 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 Linda = 31 days

And the number of days required to finish the same work by Charles = 47 days

Thus, the number of days required to finish the work Linda and Charles working together = ?

Here a = 31 days

And, b = 47 days

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

The number of days required to finish the work when Linda and Charles working together

= ^{31 × 47}/_{31 + 47} days

= ¹⁴⁵⁷/₇₈ days

= 18 ⁵³/₇₈ days or 18.679

Thus, Linda and Charles together will finish the work in 18 ⁵³/₇₈ days or 18.679 days Answer

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