In a reservoir, there are (360) litres of water in the first hour and (24) litres decrease each next hour. In which hour will the water be (96) litres?
Answer and explanation
Correct answer: 12th hour
The water quantities form an arithmetic progression with first term \(a=360\) and common difference \(d=-24\). In the \(n\)th hour, the quantity is \(a_n=360+(n-1)(-24)\). From \(360-24(n-1)=96\), we get \(24(n-1)=264\), so \(n-1=11\) and \(n=12\). Therefore, the water will be 96 litres in the 12th hour. In the 11th hour it would be 120 litres, making it a close but incorrect option. Exam tip: use a negative common difference when a quantity decreases.
Frequently asked questions
What is the correct answer to this question?
12th hour
Why is this the correct answer?
The water quantities form an arithmetic progression with first term \(a=360\) and common difference \(d=-24\). In the \(n\)th hour, the quantity is \(a_n=360+(n-1)(-24)\). From \(360-24(n-1)=96\), we get \(24(n-1)=264\), so \(n-1=11\) and \(n=12\). Therefore, the water will be 96 litres in the 12th hour. In the 11th hour it would be 120 litres, making it a close but incorrect option. Exam tip: use a negative common difference when a quantity decreases.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
