CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## For 1500 seats in the auditorium, how many rows need to be there?

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### Transcript

Question 37 (ii) – Choice 1 For 1500 seats in the auditorium, how many rows need to be there? Since Total seats = 1500 Given Sn = 1500, We need to find number of rows, i.e., we need to find n Now Sn = 𝑛/2 (2a + (n – 1)d) Putting Sn = 1500, a = 30, d = 10 1500 = 𝒏/𝟐 (2 × 30 + (n – 1) × 10) 1500 × 2 = n (60 + 10(n − 1)) 3000 = n (60 + 10n − 10) 3000 = n (50 + 10n) 3000 = 50n + 10n2 0 = 10n2 + 50n − 3000 10n2 + 50n − 3000 = 0 10(n2 + 5n − 300) = 0 n2 + 5n − 300 = 0 Solving by Splitting the middle term n2 + 20n − 15n − 300 = 0 n(n + 20) − 15(n + 20) = 0 (n − 15) (n + 20) = 0 ∴ n = 15, n = −20 Since n cannot be negative So, n = 15 Thus, number of rows is 15

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.