Time and Work
Math MCQs

Question :    If Angela can finish the work in 70 days and Terry can finish the same work in 75 days, then in how many days both can finish the work together?

Correct Answer  36 ⁶/₂₉ days or 36.207 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Angela = 70 days

And, the number of days to finish the same work by Terry = 75 days

Thus, the number of days to finish the work by Angela and Terry together = ?

Here,

∵ In 70 days the work done by Angela = 1

∴ In 1 day, the work done by Angela = ¹/₇₀ part

Similarly,

∵ In 75 days the work done by Terry = 1

∴ In 1 day, the work done by Terry = ¹/₇₅ part

Now, in 1 day, the work done by Angela and Terry together

= In 1 day work done by Angela + In 1 day the work done by Terry

= ¹/₇₀ + ¹/₇₅

= ^{15 + 14}/₁₀₅₀

= ²⁹/₁₀₅₀ part of work

This means in 1 day, ²⁹/₁₀₅₀ part of work is done by Angela and Terry working together.

Now, the number of days required to finish ²⁹/₁₀₅₀ part of work by Angela + Terry working together = 1

∴ the number of days required to finish 1 work by Angela + Terry together

= ¹/_²⁹/1050

= 1 × ¹⁰⁵⁰/₂₉ = ¹⁰⁵⁰/₂₉ days

= 36 ⁶/₂₉ days = or 36.207 days

Thus, Angela and Terry working together will finish the work in 36 ⁶/₂₉ days = or 36.207 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 Angela = 70 days

And the number of days required to finish the same work by Terry = 75 days

Thus, the number of days required to finish the work Angela and Terry working together = ?

Here a = 70 days

And, b = 75 days

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

The number of days required to finish the work when Angela and Terry working together

= ^{70 × 75}/_{70 + 75} days

= ⁵²⁵⁰/₁₄₅ days

= ^{5250 ÷ 5}/_{145 ÷ 5} = ¹⁰⁵⁰/₂₉ days

= 36 ⁶/₂₉ days or 36.207

Thus, Angela and Terry together will finish the work in 36 ⁶/₂₉ days or 36.207 days Answer

Similar Questions

(1) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(2) If Robert can finish the work in 7 days and David can finish the same work in 12 days, then in how many days both can finish the 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?

(4) If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?

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(6) If Sarah can finish the work in 19 days and Joshua can finish the same work in 22 days, then in how many days both can finish the work together?

(7) Joseph can finish a work in 19 days. Charles can finish the same work in 24 days while Christopher can finish the work in 29 days. How long will it take to finish it if they work together?

(8) Daniel can finish a work in 27 days. Anthony can finish the same work in 32 days while Mark can finish the work in 37 days. How long will it take to finish it if they work together?

(9) Charles can finish a work in 23 days. Daniel can finish the same work in 28 days while Matthew can finish the work in 33 days. How long will it take to finish it if they work together?

(10) If Angela can finish the work in 70 days and Terry can finish the same work in 75 days, then in how many days both can finish the work together?