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

(1) 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?

(2) Betty can finish a work in 26 days. Margaret can finish the same work in 27 days while Sandra can finish the work in 28 days. How long will it take to finish it if they work together?

(3) Timothy can finish a work in 49 days. Ronald can finish the same work in 50 days while Edward can finish the work in 51 days. How long will it take to finish it if they work together?

(4) If Ashley can finish the work in 33 days and Eric can finish the same work in 37 days, then in how many days both can finish the work together?

(5) If Jessica can finish the work in 17 days and Paul can finish the same work in 20 days, then in how many days both can finish the work together?

(6) If Larry can finish the work in 77 days and Lawrence can finish the same work in 82 days, then in how many days both can finish the work together?

(7) If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?

(8) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(9) If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?

(10) If Debra can finish the work in 92 days and Elijah can finish the same work in 97 days, then in how many days both can finish the work together?