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

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