Time and Work
Math MCQs

Question :    If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?

Correct Answer  36 ¹⁰⁴/₁₄₇ days or 36.707 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Eric = 71 days

And, the number of days to finish the same work by Gerald = 76 days

Thus, the number of days to finish the work by Eric and Gerald together = ?

Here,

∵ In 71 days the work done by Eric = 1

∴ In 1 day, the work done by Eric = ¹/₇₁ part

Similarly,

∵ In 76 days the work done by Gerald = 1

∴ In 1 day, the work done by Gerald = ¹/₇₆ part

Now, in 1 day, the work done by Eric and Gerald together

= In 1 day work done by Eric + In 1 day the work done by Gerald

= ¹/₇₁ + ¹/₇₆

= ^{76 + 71}/₅₃₉₆

= ¹⁴⁷/₅₃₉₆ part of work

This means in 1 day, ¹⁴⁷/₅₃₉₆ part of work is done by Eric and Gerald working together.

Now, the number of days required to finish ¹⁴⁷/₅₃₉₆ part of work by Eric + Gerald working together = 1

∴ the number of days required to finish 1 work by Eric + Gerald together

= ¹/_{¹⁴⁷/5396}

= 1 × ⁵³⁹⁶/₁₄₇ = ⁵³⁹⁶/₁₄₇ days

= 36 ¹⁰⁴/₁₄₇ days = or 36.707 days

Thus, Eric and Gerald working together will finish the work in 36 ¹⁰⁴/₁₄₇ days = or 36.707 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 Eric = 71 days

And the number of days required to finish the same work by Gerald = 76 days

Thus, the number of days required to finish the work Eric and Gerald working together = ?

Here a = 71 days

And, b = 76 days

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

The number of days required to finish the work when Eric and Gerald working together

= ^{71 × 76}/_{71 + 76} days

= ⁵³⁹⁶/₁₄₇ days

= 36 ¹⁰⁴/₁₄₇ days or 36.707

Thus, Eric and Gerald together will finish the work in 36 ¹⁰⁴/₁₄₇ days or 36.707 days Answer

Similar Questions

(1) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?

(2) If Gary can finish the work in 67 days and Christian can finish the same work in 72 days, then in how many days both can finish the work together?

(3) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?

(4) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?

(5) If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?

(6) If Myra can finish the work in 15 days and Sophia can finish the same work in 20 days, then in how many days they both can finish the work working together?

(7) If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?

(8) If Richard can finish the work in 17 days and Mark can finish the same work in 22 days, then in how many days both can finish the work together?

(9) 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?

(10) John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?