Two friends together complete a work in (12\text{ days}). The first friend alone takes (10\text{ days}) less than the second. How many days will the first friend alone take?

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Answer and explanation

Correct answer: (20\text{ days})

Let the first friend's time be (x), so the second's is (x+10), and (\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}). This gives (x^2-14x-120=0), so (x=20).

What is the correct answer to this question?

(20\text{ days})

Why is this the correct answer?

Let the first friend's time be (x), so the second's is (x+10), and (\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}). This gives (x^2-14x-120=0), so (x=20).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.

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