In a tank (52) litres of water are filled in the first minute and (16) litres more in each next minute. In which minute will (308) litres be filled?
Answer and explanation
Correct answer: 17th minute
The amount filled each minute forms an AP with first term \(a=52\) and common difference \(d=16\). Thus, the amount filled in the \(n\)th minute is \(a_n=52+(n-1)16\). Setting this equal to \(308\), \(52+(n-1)16=308\), so \((n-1)16=256\), \(n-1=16\), and \(n=17\). Therefore, 308 litres are filled in the 17th minute. In the 16th minute, the amount is \(292\) litres, so that close option is incorrect. Exam tip: distinguish between the amount filled in a particular minute and the total amount filled up to that minute.
Frequently asked questions
What is the correct answer to this question?
17th minute
Why is this the correct answer?
The amount filled each minute forms an AP with first term \(a=52\) and common difference \(d=16\). Thus, the amount filled in the \(n\)th minute is \(a_n=52+(n-1)16\). Setting this equal to \(308\), \(52+(n-1)16=308\), so \((n-1)16=256\), \(n-1=16\), and \(n=17\). Therefore, 308 litres are filled in the 17th minute. In the 16th minute, the amount is \(292\) litres, so that close option is incorrect. Exam tip: distinguish between the amount filled in a particular minute and the total amount filled up to that minute.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
