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Class 10 AP Word Problems — practice questions with answers

Algebra — Sequences · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Ravi saves Rs 100 in the first month and increases his saving by Rs 50 every month. How much does he save in the 5th month?
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Answer: B) Rs 300
a = 100, d = 50. a5 = 100 + 4(50) = 100 + 200 = Rs 300.
2. The houses on Gandhi Road are numbered 1, 2, 3, ..., 49. What is the sum of all the house numbers?
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Answer: A) 1225
S = (first + last) = (1 + 49) = (50) = 49 x 25 = 1225.
3. The production of TV sets in a factory increases uniformly by a fixed number every year.
In the 3rd year production was 600 sets and in the 7th year it was 700 sets.
Find the production in the 1st year.
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Answer: C) 550
a7 - a3 = 4d = 700 - 600 = 100, so d = 25. a3 = a + 2d = 600 gives a = 600 - 50 = 550.
4. Pooja's monthly electricity bill rose in AP: Rs 800 in January and Rs 1280 in July (the 7th month).
What was her bill in April (the 4th month)?
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Answer: D) 1040
a = 800, a7 = 1280 so 6d = 480, d = 80. a4 = 800 + 3(80) = 800 + 240 = Rs 1040.
5. A stadium seats people in rows so that row 1 seats 20 people and each higher row seats 4 more.
The stadium fills exactly 2340 people across all rows.
How many rows are there?
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Answer: A) 30
a = 20, d = 4. Sn = [40+(n-1)4] = (36+4n) = n(18+2n) = 2340, so 2n² + 18n - 2340 = 0, n² + 9n - 1170 = 0. Factor: (n-30)(n+39) = 0, so n = 30 rows.
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