Time and Work
Math MCQs

Question :    If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?

Correct Answer  37 ³¹/₁₄₉ days or 37.208 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Shirley = 72 days

And, the number of days to finish the same work by Harold = 77 days

Thus, the number of days to finish the work by Shirley and Harold together = ?

Here,

∵ In 72 days the work done by Shirley = 1

∴ In 1 day, the work done by Shirley = ¹/₇₂ part

Similarly,

∵ In 77 days the work done by Harold = 1

∴ In 1 day, the work done by Harold = ¹/₇₇ part

Now, in 1 day, the work done by Shirley and Harold together

= In 1 day work done by Shirley + In 1 day the work done by Harold

= ¹/₇₂ + ¹/₇₇

= ^{77 + 72}/₅₅₄₄

= ¹⁴⁹/₅₅₄₄ part of work

This means in 1 day, ¹⁴⁹/₅₅₄₄ part of work is done by Shirley and Harold working together.

Now, the number of days required to finish ¹⁴⁹/₅₅₄₄ part of work by Shirley + Harold working together = 1

∴ the number of days required to finish 1 work by Shirley + Harold together

= ¹/_{¹⁴⁹/5544}

= 1 × ⁵⁵⁴⁴/₁₄₉ = ⁵⁵⁴⁴/₁₄₉ days

= 37 ³¹/₁₄₉ days = or 37.208 days

Thus, Shirley and Harold working together will finish the work in 37 ³¹/₁₄₉ days = or 37.208 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 Shirley = 72 days

And the number of days required to finish the same work by Harold = 77 days

Thus, the number of days required to finish the work Shirley and Harold working together = ?

Here a = 72 days

And, b = 77 days

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

The number of days required to finish the work when Shirley and Harold working together

= ^{72 × 77}/_{72 + 77} days

= ⁵⁵⁴⁴/₁₄₉ days

= 37 ³¹/₁₄₉ days or 37.208

Thus, Shirley and Harold together will finish the work in 37 ³¹/₁₄₉ days or 37.208 days Answer

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