Time and Work
Math MCQs

Question :    If Helen can finish the work in 84 days and Bruce can finish the same work in 89 days, then in how many days both can finish the work together?

Correct Answer  43 ³⁷/₁₇₃ days or 43.214 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Helen = 84 days

And, the number of days to finish the same work by Bruce = 89 days

Thus, the number of days to finish the work by Helen and Bruce together = ?

Here,

∵ In 84 days the work done by Helen = 1

∴ In 1 day, the work done by Helen = ¹/₈₄ part

Similarly,

∵ In 89 days the work done by Bruce = 1

∴ In 1 day, the work done by Bruce = ¹/₈₉ part

Now, in 1 day, the work done by Helen and Bruce together

= In 1 day work done by Helen + In 1 day the work done by Bruce

= ¹/₈₄ + ¹/₈₉

= ^{89 + 84}/₇₄₇₆

= ¹⁷³/₇₄₇₆ part of work

This means in 1 day, ¹⁷³/₇₄₇₆ part of work is done by Helen and Bruce working together.

Now, the number of days required to finish ¹⁷³/₇₄₇₆ part of work by Helen + Bruce working together = 1

∴ the number of days required to finish 1 work by Helen + Bruce together

= ¹/_¹⁷³/7476

= 1 × ⁷⁴⁷⁶/₁₇₃ = ⁷⁴⁷⁶/₁₇₃ days

= 43 ³⁷/₁₇₃ days = or 43.214 days

Thus, Helen and Bruce working together will finish the work in 43 ³⁷/₁₇₃ days = or 43.214 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 Helen = 84 days

And the number of days required to finish the same work by Bruce = 89 days

Thus, the number of days required to finish the work Helen and Bruce working together = ?

Here a = 84 days

And, b = 89 days

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

The number of days required to finish the work when Helen and Bruce working together

= ^{84 × 89}/_{84 + 89} days

= ⁷⁴⁷⁶/₁₇₃ days

= 43 ³⁷/₁₇₃ days or 43.214

Thus, Helen and Bruce together will finish the work in 43 ³⁷/₁₇₃ days or 43.214 days Answer

Similar Questions

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(2) Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?

(3) Patrick can finish a work in 95 days. Jack can finish the same work in 100 days while Dennis can finish the work in 105 days. How long will it take to finish it if they work together?

(4) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

(5) If Anthony can finish the work in 31 days and Jeffrey can finish the same work in 36 days, then in how many days both can finish the work together?

(6) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(7) Charles can finish a work in 23 days. Daniel can finish the same work in 28 days while Matthew can finish the work in 33 days. How long will it take to finish it if they work together?

(8) 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?

(9) If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?

(10) Michelle can finish a work in 44 days. Amanda can finish the same work in 49 days while Dorothy can finish the work in 54 days. How long will it take to finish it if they work together?