Time and Work
Math MCQs

Question :    Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?

Correct Answer  33 ²⁹⁴⁸⁷/₃₁₁₈₇ days or 33.945 days

Solution & Explanation

Solution

Given,

The number of days required to finish a piece of work by Raymond = 97 days

And, the number of days required to finish the same work by Dennis = 102 days

And, the number of days required to finish the same work by Jerry = 107 days

Thus, the number of days required to finish the work by all of them if they work together = ?

Here,

∵ In 97 days the work is done by Raymond = 1

∴ The work done by Raymond in 1 day = ¹/₉₇

Similarly,

∵ In 102 days the work is done by Dennis = 1

∴ The work done by Dennis in 1 day = ¹/₁₀₂

Similarly,

∵ In 107 days the work is done by Jerry = 1

∴ The work done by Jerry in 1 day = ¹/₁₀₇ part

Now, the work done by Raymond, Dennis, and Jerry together in 1 day

= Raymond's 1 day work + Dennis's 1 day work + Jerry's 1 day work

= ¹/₉₇ + ¹/₁₀₂ + ¹/₁₀₇

= ^{10914 + 10379 + 9894}/_1058658

= ³¹¹⁸⁷/_1058658 part of work

This means in 1 day, ³¹¹⁸⁷/_1058658 part of work is done by Raymond, Dennis and Jerry working together.

Now, the number of days required to finish ³¹¹⁸⁷/_1058658 part of work by Raymond, Dennis, and Jerry working together = 1

∴ the number of days required to finish the whole work (1 work) by Raymond + Dennis + Jerry together

= ¹/_{³¹¹⁸⁷/1058658}

= 1 × ^1058658/₃₁₁₈₇ = ^1058658/₃₁₁₈₇ days

= 33 ²⁹⁴⁸⁷/₃₁₁₈₇ days = or 33.945 days

Thus, Raymond, Dennis, and Jerry working together will finish the total work (1 work) in 33 ²⁹⁴⁸⁷/₃₁₁₈₇ days = or 33.945 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= ^{a × b × c}/_{ab + ac + bc} days.

Here given,

The number of days required to finish the work by Raymond = 97 days

And the number of days required to finish the same work by Dennis = 102 days

And the number of days required to finish the work by Jerry = 107 days

Thus, the number of days required to finish the work by Raymond, Dennis, and Jerry together = ?

Here a = 97 days

And, b = 102 days

And, c = 107 days

Thus, using formula ^{a × b × c}/_{ab + ac + bc} days

The number of days required to finish the work when Raymond, Dennis, and Jerry working together

= ^{97 × 102 × 107}/_{97 × 102 + 97 × 107 + 102 × 107} days

= ^1058658/_{9894 + 10379 + 10914} days

= ^1058658/₃₁₁₈₇ days

= ^1058658/₃₁₁₈₇ days

= 33 ²⁹⁴⁸⁷/₃₁₁₈₇ days or 33.945

Thus, Raymond, Dennis, and Jerry together will finish the work in 33 ²⁹⁴⁸⁷/₃₁₁₈₇ days or 33.945 days Answer

Similar Questions

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