Time and Work
Math MCQs

Question :    If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?

Correct Answer  24 ¹⁸/₉₇ days or 24.186 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Carol = 46 days

And, the number of days to finish the same work by Alexander = 51 days

Thus, the number of days to finish the work by Carol and Alexander together = ?

Here,

∵ In 46 days the work done by Carol = 1

∴ In 1 day, the work done by Carol = ¹/₄₆ part

Similarly,

∵ In 51 days the work done by Alexander = 1

∴ In 1 day, the work done by Alexander = ¹/₅₁ part

Now, in 1 day, the work done by Carol and Alexander together

= In 1 day work done by Carol + In 1 day the work done by Alexander

= ¹/₄₆ + ¹/₅₁

= ^{51 + 46}/₂₃₄₆

= ⁹⁷/₂₃₄₆ part of work

This means in 1 day, ⁹⁷/₂₃₄₆ part of work is done by Carol and Alexander working together.

Now, the number of days required to finish ⁹⁷/₂₃₄₆ part of work by Carol + Alexander working together = 1

∴ the number of days required to finish 1 work by Carol + Alexander together

= ¹/_⁹⁷/2346

= 1 × ²³⁴⁶/₉₇ = ²³⁴⁶/₉₇ days

= 24 ¹⁸/₉₇ days = or 24.186 days

Thus, Carol and Alexander working together will finish the work in 24 ¹⁸/₉₇ days = or 24.186 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 Carol = 46 days

And the number of days required to finish the same work by Alexander = 51 days

Thus, the number of days required to finish the work Carol and Alexander working together = ?

Here a = 46 days

And, b = 51 days

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

The number of days required to finish the work when Carol and Alexander working together

= ^{46 × 51}/_{46 + 51} days

= ²³⁴⁶/₉₇ days

= 24 ¹⁸/₉₇ days or 24.186

Thus, Carol and Alexander together will finish the work in 24 ¹⁸/₉₇ days or 24.186 days Answer

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