Time and Work
Math MCQs

Question :    If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?

Correct Answer  8 ¹³/₃₄ days or 8.382 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Susan = 15 days

And, the number of days to finish the same work by Donald = 19 days

Thus, the number of days to finish the work by Susan and Donald together = ?

Here,

∵ In 15 days the work done by Susan = 1

∴ In 1 day, the work done by Susan = ¹/₁₅ part

Similarly,

∵ In 19 days the work done by Donald = 1

∴ In 1 day, the work done by Donald = ¹/₁₉ part

Now, in 1 day, the work done by Susan and Donald together

= In 1 day work done by Susan + In 1 day the work done by Donald

= ¹/₁₅ + ¹/₁₉

= ^{19 + 15}/₂₈₅

= ³⁴/₂₈₅ part of work

This means in 1 day, ³⁴/₂₈₅ part of work is done by Susan and Donald working together.

Now, the number of days required to finish ³⁴/₂₈₅ part of work by Susan + Donald working together = 1

∴ the number of days required to finish 1 work by Susan + Donald together

= ¹/_³⁴/285

= 1 × ²⁸⁵/₃₄ = ²⁸⁵/₃₄ days

= 8 ¹³/₃₄ days = or 8.382 days

Thus, Susan and Donald working together will finish the work in 8 ¹³/₃₄ days = or 8.382 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 Susan = 15 days

And the number of days required to finish the same work by Donald = 19 days

Thus, the number of days required to finish the work Susan and Donald working together = ?

Here a = 15 days

And, b = 19 days

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

The number of days required to finish the work when Susan and Donald working together

= ^{15 × 19}/_{15 + 19} days

= ²⁸⁵/₃₄ days

= 8 ¹³/₃₄ days or 8.382

Thus, Susan and Donald together will finish the work in 8 ¹³/₃₄ days or 8.382 days Answer

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