A worker completes 180 units of work in x days by completing x + 3 units each day. What is the number of days?
Answer and explanation
Correct answer: 12 days
The governing concept is the work relation: total work equals the number of days multiplied by the work completed each day. Here, the total work is 180 units, the number of days is x, and the daily work is x + 3. Therefore, x(x + 3) = 180, which gives x² + 3x − 180 = 0. Factoring, (x + 15)(x − 12) = 0, so x = −15 or x = 12. A duration cannot be negative, so x = 12 is the meaningful solution. The worker therefore takes 12 days and completes 15 units per day; 12 × 15 = 180 verifies the answer. The other options do not satisfy the complete work equation.
Frequently asked questions
What is the correct answer to this question?
12 days
Why is this the correct answer?
The governing concept is the work relation: total work equals the number of days multiplied by the work completed each day. Here, the total work is 180 units, the number of days is x, and the daily work is x + 3. Therefore, x(x + 3) = 180, which gives x² + 3x − 180 = 0. Factoring, (x + 15)(x − 12) = 0, so x = −15 or x = 12. A duration cannot be negative, so x = 12 is the meaningful solution. The worker therefore takes 12 days and completes 15 units per day; 12 × 15 = 180 verifies the answer. The other options do not satisfy the complete work equation.
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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