Time and Work
Math MCQs

Question :    If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?

Correct Answer  7 ¹⁷/₃₁ days or 7.548 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by David = 13 days

And, the number of days to finish the same work by Christopher = 18 days

Thus, the number of days to finish the work by David and Christopher together = ?

Here,

∵ In 13 days the work done by David = 1

∴ In 1 day, the work done by David = ¹/₁₃ part

Similarly,

∵ In 18 days the work done by Christopher = 1

∴ In 1 day, the work done by Christopher = ¹/₁₈ part

Now, in 1 day, the work done by David and Christopher together

= In 1 day work done by David + In 1 day the work done by Christopher

= ¹/₁₃ + ¹/₁₈

= ^{18 + 13}/₂₃₄

= ³¹/₂₃₄ part of work

This means in 1 day, ³¹/₂₃₄ part of work is done by David and Christopher working together.

Now, the number of days required to finish ³¹/₂₃₄ part of work by David + Christopher working together = 1

∴ the number of days required to finish 1 work by David + Christopher together

= ¹/_³¹/234

= 1 × ²³⁴/₃₁ = ²³⁴/₃₁ days

= 7 ¹⁷/₃₁ days = or 7.548 days

Thus, David and Christopher working together will finish the work in 7 ¹⁷/₃₁ days = or 7.548 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 David = 13 days

And the number of days required to finish the same work by Christopher = 18 days

Thus, the number of days required to finish the work David and Christopher working together = ?

Here a = 13 days

And, b = 18 days

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

The number of days required to finish the work when David and Christopher working together

= ^{13 × 18}/_{13 + 18} days

= ²³⁴/₃₁ days

= 7 ¹⁷/₃₁ days or 7.548

Thus, David and Christopher together will finish the work in 7 ¹⁷/₃₁ days or 7.548 days Answer

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