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 Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?

(2) Linda can finish a work in 8 days. Elizabeth can finish the same work in 9 days while Barbara can finish the work in 10 days. How long will it take to finish it if they work together?

(3) 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?

(4) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?

(5) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?

(6) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

(7) 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?

(8) 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?

(9) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?

(10) Kenneth can finish a work in 41 days. Kevin can finish the same work in 42 days while Brian can finish the work in 43 days. How long will it take to finish it if they work together?