Home > Arithmetic Progressions > CBSE_BOARD_PYQ_2026_30_7_1 > 5b62ac1b-7f8e-5461-9665-e68c3f634d70
Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Arithmetic Progressions
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10

Question:

[Section E]

Case Study 1: Factory Production Rate

A bicycle manufacturer increases production uniformly by a fixed number of sets every year. The factory produced $270$ bicycles in the $4^{\text{th}}$ year and $510$ bicycles in the $10^{\text{th}}$ year.

1. Find the production of bicycles in the $1^{\text{st}}$ year. (1 Mark)
2. Find the production in the $8^{\text{th}}$ year. (1 Mark)
3. Find the total production of bicycles in the first $6$ years. (2 Marks)

OR (for part 3)

3. Find the ratio of the production in the $2^{\text{nd}}$ year to the production in the $8^{\text{th}}$ year. (2 Marks)

Step-by-Step Solution

Key Concept: AP equations: $a + 3d = 270$ and $a + 9d = 510 \Rightarrow d = 40, a = 150$.
$a + 3d = 270$ and $a + 9d = 510 \Rightarrow d = 40, a = 150$.
1. Production in 1st year $a = 150$. [1.0 Mark]

2. Production in 8th year $a_8 = 150 + 7(40) = 430$. [1.0 Mark]

[Part 3 Main] $S_6 = \dfrac{6}{2}[2(150) + 5(40)] = 3(300 + 200) = 1500$. [2.0 Marks]


-------------------------------


[Part 3 OR Choice]
$a_2 = 150 + 40 = 190$. Ratio $a_2 : a_8 = 190 : 430 = 19 : 43$. [2.0 Marks]

Correct Answer: 1. 150 bicycles, 2. 430 bicycles, 3. 1500 bicycles (OR Ratio 19 : 43)
Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.

Master Arithmetic Progressions with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free