Time and Work
Math MCQs

Question :    If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?

Correct Answer  29 ⁸³/₁₁₉ days or 29.697 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Edward = 57 days

And, the number of days to finish the same work by Nathan = 62 days

Thus, the number of days to finish the work by Edward and Nathan together = ?

Here,

∵ In 57 days the work done by Edward = 1

∴ In 1 day, the work done by Edward = ¹/₅₇ part

Similarly,

∵ In 62 days the work done by Nathan = 1

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

Now, in 1 day, the work done by Edward and Nathan together

= In 1 day work done by Edward + In 1 day the work done by Nathan

= ¹/₅₇ + ¹/₆₂

= ^{62 + 57}/₃₅₃₄

= ¹¹⁹/₃₅₃₄ part of work

This means in 1 day, ¹¹⁹/₃₅₃₄ part of work is done by Edward and Nathan working together.

Now, the number of days required to finish ¹¹⁹/₃₅₃₄ part of work by Edward + Nathan working together = 1

∴ the number of days required to finish 1 work by Edward + Nathan together

= ¹/_¹¹⁹/3534

= 1 × ³⁵³⁴/₁₁₉ = ³⁵³⁴/₁₁₉ days

= 29 ⁸³/₁₁₉ days = or 29.697 days

Thus, Edward and Nathan working together will finish the work in 29 ⁸³/₁₁₉ days = or 29.697 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 Edward = 57 days

And the number of days required to finish the same work by Nathan = 62 days

Thus, the number of days required to finish the work Edward and Nathan working together = ?

Here a = 57 days

And, b = 62 days

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

The number of days required to finish the work when Edward and Nathan working together

= ^{57 × 62}/_{57 + 62} days

= ³⁵³⁴/₁₁₉ days

= 29 ⁸³/₁₁₉ days or 29.697

Thus, Edward and Nathan together will finish the work in 29 ⁸³/₁₁₉ days or 29.697 days Answer

Similar Questions

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