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Case Study – 3
A road roller is a compactor-type engineering vehicle, used to compact soil, gravel, concrete, etc, in the construction of roads and foundations. They are also used at landfills or in agriculture. A company started making road rollers $10$ years ago and increased its production uniformly by a fixed number every year. The company produces $800$ rollers in the $6^{th}$ year and $1130$ rollers in the $9^{th}$ year.
Based on the above information, answer the following questions :
(i) What is the company's production in the first year ?
(ii) What was the increase in the company's production every year?
(iii) (a) What was the company's production in the $8^{th}$ year?
OR
(b) What was the company's total production in the first $6$ years?
A road roller is a compactor-type engineering vehicle, used to compact soil, gravel, concrete, etc, in the construction of roads and foundations. They are also used at landfills or in agriculture. A company started making road rollers $10$ years ago and increased its production uniformly by a fixed number every year. The company produces $800$ rollers in the $6^{th}$ year and $1130$ rollers in the $9^{th}$ year.
Based on the above information, answer the following questions :
(i) What is the company's production in the first year ?
(ii) What was the increase in the company's production every year?
(iii) (a) What was the company's production in the $8^{th}$ year?
OR
(b) What was the company's total production in the first $6$ years?
Show SolutionHide Solution↓
(i) $$\begin{aligned}& (a + 8d) - (a + 5d) = 330 \Rightarrow d = 110 \\ & a+5\times110 = 800 \Rightarrow a = 250 \\ & (ii) d=110 \\ & (iii) (a)\end{aligned}$$a_8 = 250 + 7
times 110
= 1020
OR
(iii) (b) $$\begin{aligned}& S_6 = \frac{6}{2} [2 \times 250 + 5 \times 110] \\ & = 3150\end{aligned}$$
times 110
= 1020
OR
(iii) (b) $$\begin{aligned}& S_6 = \frac{6}{2} [2 \times 250 + 5 \times 110] \\ & = 3150\end{aligned}$$