Time and Work
Math MCQs

Question :    If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?

Correct Answer  14 ⁴/₁₉ days or 14.211 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Betty = 27 days

And, the number of days to finish the same work by Jason = 30 days

Thus, the number of days to finish the work by Betty and Jason together = ?

Here,

∵ In 27 days the work done by Betty = 1

∴ In 1 day, the work done by Betty = ¹/₂₇ part

Similarly,

∵ In 30 days the work done by Jason = 1

∴ In 1 day, the work done by Jason = ¹/₃₀ part

Now, in 1 day, the work done by Betty and Jason together

= In 1 day work done by Betty + In 1 day the work done by Jason

= ¹/₂₇ + ¹/₃₀

= ^{10 + 9}/₂₇₀

= ¹⁹/₂₇₀ part of work

This means in 1 day, ¹⁹/₂₇₀ part of work is done by Betty and Jason working together.

Now, the number of days required to finish ¹⁹/₂₇₀ part of work by Betty + Jason working together = 1

∴ the number of days required to finish 1 work by Betty + Jason together

= ¹/_¹⁹/270

= 1 × ²⁷⁰/₁₉ = ²⁷⁰/₁₉ days

= 14 ⁴/₁₉ days = or 14.211 days

Thus, Betty and Jason working together will finish the work in 14 ⁴/₁₉ days = or 14.211 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 Betty = 27 days

And the number of days required to finish the same work by Jason = 30 days

Thus, the number of days required to finish the work Betty and Jason working together = ?

Here a = 27 days

And, b = 30 days

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

The number of days required to finish the work when Betty and Jason working together

= ^{27 × 30}/_{27 + 30} days

= ⁸¹⁰/₅₇ days

= ^{810 ÷ 3}/_{57 ÷ 3} = ²⁷⁰/₁₉ days

= 14 ⁴/₁₉ days or 14.211

Thus, Betty and Jason together will finish the work in 14 ⁴/₁₉ days or 14.211 days Answer

Similar Questions

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(2) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?

(3) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

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(6) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?

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(8) If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?

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(10) If Mark can finish the work in 33 days and Jacob can finish the same work in 38 days, then in how many days both can finish the work together?