A reservoir has (210) litres of water on the first day and (12) litres less each next day. On which day will (66) litres remain?
Answer and explanation
Correct answer: 13
The amount of water forms a decreasing AP with \(a=210\) and \(d=-12\). On the \(n\)th day, \(a_n=210+(n-1)(-12)\). Solving \(210-12(n-1)=66\) gives \(n-1=12\), so \(n=13\). Therefore, 66 litres remain on the 13th day. On the 12th day, the amount is 78 litres, so option 12 is not correct. Exam tip: use a negative common difference \(d\) for a decreasing AP.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
The amount of water forms a decreasing AP with \(a=210\) and \(d=-12\). On the \(n\)th day, \(a_n=210+(n-1)(-12)\). Solving \(210-12(n-1)=66\) gives \(n-1=12\), so \(n=13\). Therefore, 66 litres remain on the 13th day. On the 12th day, the amount is 78 litres, so option 12 is not correct. Exam tip: use a negative common difference \(d\) for a decreasing AP.
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.
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