Time and Work
Math MCQs

Question :    If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?

Correct Answer  16 ²/₁₃ days or 16.154 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Betty = 30 days

And, the number of days to finish the same work by Jason = 35 days

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

Here,

∵ In 30 days the work done by Betty = 1

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

Similarly,

∵ In 35 days the work done by Jason = 1

∴ In 1 day, the work done by Jason = ¹/₃₅ 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

= ¹/₃₀ + ¹/₃₅

= ^{7 + 6}/₂₁₀

= ¹³/₂₁₀ part of work

This means in 1 day, ¹³/₂₁₀ part of work is done by Betty and Jason working together.

Now, the number of days required to finish ¹³/₂₁₀ part of work by Betty + Jason working together = 1

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

= ¹/_¹³/210

= 1 × ²¹⁰/₁₃ = ²¹⁰/₁₃ days

= 16 ²/₁₃ days = or 16.154 days

Thus, Betty and Jason working together will finish the work in 16 ²/₁₃ days = or 16.154 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 = 30 days

And the number of days required to finish the same work by Jason = 35 days

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

Here a = 30 days

And, b = 35 days

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

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

= ^{30 × 35}/_{30 + 35} days

= ¹⁰⁵⁰/₆₅ days

= ^{1050 ÷ 5}/_{65 ÷ 5} = ²¹⁰/₁₃ days

= 16 ²/₁₃ days or 16.154

Thus, Betty and Jason together will finish the work in 16 ²/₁₃ days or 16.154 days Answer

Similar Questions

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(2) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?

(3) If John can finish the work in 28 days and Richard can finish the same work in 44 days, then in how many days both can finish the work together?

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(5) If Nancy can finish the work in 25 days and Ronald can finish the same work in 29 days, then in how many days both can finish the work together?

(6) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 46 days, then in how many days both can finish the work together?

(7) Kimberly can finish a work in 38 days. Donna can finish the same work in 43 days while Michelle can finish the work in 48 days. How long will it take to finish it if they work together?

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