A farmer sells (95) kg grain in the first week and (18) kg more each next week. In which week will (311) kg grain be sold?
Answer and explanation
Correct answer: (13)
The weekly sales form an AP with first term \(a=95\) and common difference \(d=18\). The sale in the \(n\)th week is \(a_n=95+(n-1)18\). Setting this equal to 311 gives \(95+(n-1)18=311\), so \(18(n-1)=216\), \(n-1=12\), and \(n=13\). Therefore, 311 kg will be sold in the 13th week. In the 12th week, the sale would be \(293\) kg, so it is a close but incorrect option. Exam tip: equate the target quantity to \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
(13)
Why is this the correct answer?
The weekly sales form an AP with first term \(a=95\) and common difference \(d=18\). The sale in the \(n\)th week is \(a_n=95+(n-1)18\). Setting this equal to 311 gives \(95+(n-1)18=311\), so \(18(n-1)=216\), \(n-1=12\), and \(n=13\). Therefore, 311 kg will be sold in the 13th week. In the 12th week, the sale would be \(293\) kg, so it is a close but incorrect option. Exam tip: equate the target quantity to \(a_n\) and solve for \(n\).
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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