Question

17. A road roller (sometimes called a roller-compactor, or just roller) is a
compactor-type engineering vehicle used to compact soil, gravel, concrete, or
asphalt in the construction of roads and foundations. Similar rollers are used also
at landfills or in agriculture. Road rollers are frequently referred to as
steamrollers, regardless of their method of propulsion.

RCB Machine Pvt Ltd started making road roller 10 year ago. Company increased
its production uniformly by fixed number every year. The company produces 800
roller in the 6th year and 1130 roller in the 9th year.
On the basis of the above information, answer any four of the following
questions:

(i) What was the company’s production in first year?
(a) 150
(b) 200
(c) 250
(d) 290

(ii) What was the company’s production in the 8th year?
(a) 760
(b) 820
(c) 880
(d) 1020

(iii) What roller the company’s total production of the first 6 years?
(a) 3150
(b) 1775
(c) 2250
(d) 1725


(iv) What was the increase in the company’s production every year?
(a) 160
(b) 130
(c) 90
(d) 110

(v) In which year the company’s production was 1350 rollers?
(a) 5th
(b) 6th
(c) 11th
(d) 9th

Answer 1

(i) (c) 250

(ii) (d) 1020

(iii) (a) 3150

(iv) (d) 110

(v) (c) 11th

With the help of the given information, we can form an Arithmetic Progression whose first term is a and the common difference is d.

Given, production in the 6th year is 800 and production in 9th year is 1130

⇒ a + 5d = 800 ... ... (1)

and a + 8d = 1130 ... ... (2)

Now, (2) - (1) gives

3d = 330

⇒ d = 110

Putting d = 110 in (1), we get

a + 5 (110) = 800

⇒ a + 550 = 800

⇒ a = 250

(i) Production in first year :

The production in first year was 250.

(ii) Production in the 8th year :

The company's production in the 8th year was

a + 7d

= 250 + 7 (110)

= 250 + 770

= 1020

(iii) Total production of the first 6 years :

Total production of the first 6 years

= $\dfrac{6}{2}[2\times 250+(6-1)\times 110]$

= 3 [500 + 550]

= 3 [1050]

= 3150

(iv) Increase in production every year :

The increase in production every year was 110.

(v) The year in which production was 1350 :

Let the it be the nth year. Then

a + (n - 1) d = 1350

⇒ 250 + (n - 1) 110 = 1350

⇒ (n - 1) 110 = 1100

⇒ n - 1 = 10

⇒ n = 11

Answer 2

Answer:

1.250

2.1020

3. 3150

4. 110

5. 11