A student solves 64 questions on the first day and 15 more questions each day. On which day will he solve 514 questions?
Answer and explanation
Correct answer: 31वाँ
The number solved each day forms an arithmetic progression: 64, 79, 94, …, with first term a₁ = 64 and common difference d = 15. We are looking for the daily number, so we use the nth-term formula rather than the sum formula. Set aₙ = 514: 514 = 64 + (n − 1)15. Subtracting 64 gives 450 = 15(n − 1). Dividing by 15 gives n − 1 = 30, hence n = 31. A direct check gives the 31st-day value as 64 + 30 × 15 = 514. Therefore, option C, the 31st day, is correct. The nearby choices arise if one counts the first day incorrectly or confuses the number solved on a day with the cumulative total solved over several days.
Frequently asked questions
What is the correct answer to this question?
31वाँ
Why is this the correct answer?
The number solved each day forms an arithmetic progression: 64, 79, 94, …, with first term a₁ = 64 and common difference d = 15. We are looking for the daily number, so we use the nth-term formula rather than the sum formula. Set aₙ = 514: 514 = 64 + (n − 1)15. Subtracting 64 gives 450 = 15(n − 1). Dividing by 15 gives n − 1 = 30, hence n = 31. A direct check gives the 31st-day value as 64 + 30 × 15 = 514. Therefore, option C, the 31st day, is correct. The nearby choices arise if one counts the first day incorrectly or confuses the number solved on a day with the cumulative total solved over several days.
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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