In a row arrangement the first row has 25 students and 22 rows have 1243 students in total. If the increase is equal then what is the increase?
Answer and explanation
Correct answer: 3
The row sizes form an arithmetic progression. The first term is a = 25, the number of rows is n = 22, and the total is S_22 = 1243. Using S_n = n/2[2a + (n - 1)d], we get 1243 = 22/2[2(25) + 21d] = 11(50 + 21d). Dividing by 11 gives 113 = 50 + 21d, so 21d = 63 and d = 3. Therefore, option B is correct. The other choices do not satisfy the given total: substituting any of them into the sum formula produces a total different from 1243.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The row sizes form an arithmetic progression. The first term is a = 25, the number of rows is n = 22, and the total is S_22 = 1243. Using S_n = n/2[2a + (n - 1)d], we get 1243 = 22/2[2(25) + 21d] = 11(50 + 21d). Dividing by 11 gives 113 = 50 + 21d, so 21d = 63 and d = 3. Therefore, option B is correct. The other choices do not satisfy the given total: substituting any of them into the sum formula produces a total different from 1243.
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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