Time and Work
MCQs Math


Question:     If Sarah can finish the work in 19 days and Joshua can finish the same work in 23 days, then in how many days both can finish the work together?


Correct Answer  10 17/42 days or 10.405 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Sarah = 19 days

And, the number of days to finish the same work by Joshua = 23 days

Thus, the number of days to finish the work by Sarah and Joshua together = ?

Here,

∵ In 19 days the work done by Sarah = 1

∴ In 1 day, the work done by Sarah = 1/19 part

Similarly,

∵ In 23 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = 1/23 part

Now, in 1 day, the work done by Sarah and Joshua together

= In 1 day work done by Sarah + In 1 day the work done by Joshua

= 1/19 + 1/23

= 23 + 19/437

= 42/437 part of work

This means in 1 day, 42/437 part of work is done by Sarah and Joshua working together.

Now, the number of days required to finish 42/437 part of work by Sarah + Joshua working together = 1

∴ the number of days required to finish 1 work by Sarah + Joshua together

= 1/42/437

= 1 × 437/42 = 437/42 days

= 10 17/42 days = or 10.405 days

Thus, Sarah and Joshua working together will finish the work in 10 17/42 days = or 10.405 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 Sarah = 19 days

And the number of days required to finish the same work by Joshua = 23 days

Thus, the number of days required to finish the work Sarah and Joshua working together = ?

Here a = 19 days

And, b = 23 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Sarah and Joshua working together

= 19 × 23/19 + 23 days

= 437/42 days

= 10 17/42 days or 10.405

Thus, Sarah and Joshua together will finish the work in 10 17/42 days or 10.405 days Answer


Similar Questions

(1) Cynthia can finish a work in 64 days. Amy can finish the same work in 69 days while Angela can finish the work in 74 days. How long will it take to finish it if they work together?

(2) Daniel can finish a work in 23 days. Matthew can finish the same work in 24 days while Anthony can finish the work in 25 days. How long will it take to finish it if they work together?

(3) If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?

(4) Frank can finish a work in 93 days. Raymond can finish the same work in 98 days while Jack can finish the work in 103 days. How long will it take to finish it if they work together?

(5) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(6) Jessica can finish a work in 16 days. Sarah can finish the same work in 17 days while Karen can finish the work in 18 days. How long will it take to finish it if they work together?

(7) Emily can finish a work in 36 days. Donna can finish the same work in 37 days while Michelle can finish the work in 38 days. How long will it take to finish it if they work together?

(8) Angela can finish a work in 70 days. Anna can finish the same work in 75 days while Brenda can finish the work in 80 days. How long will it take to finish it if they work together?

(9) Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?

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