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

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