Question

7. Excavators are important and widely used equipment in construction industry. Their general purpose
is to excavate but other than that they are also used for many purpose like heavy lifting, demolition
river dredging, cutting of trees etc. ABC Machinery Pvt: Lid. Started making excavators about 15
years ago. The company increased its production uniformly by a fixed number every year. The
company produces 700 excavators in the si" year and 1180 excavators in the 11 year,
i)
What was the company production of excavators in the first year?
guya) 240
b) 340
c) 380
d) 460
What was the company's production in the 6 year?
a) 780
b) 1560
c) 1320
d) 2240
What was the total production of excavators in the first 8 years?
a) 2640
b) 3280
c) 10560
d) 5280
In which year the company's production was 1340 excavators?
year
The sum of last ten terms of the AP 8,10,12,...,126 is
a) 4020
b) 2010 c) 1148
d) 1170

​

Answer 1

To find the company's production of excavators in the first year, we can use the fact that the company increased its production uniformly by a fixed number every year.

Since the company produces 700 excavators in the 11th year and 1180 excavators in the 11th year, we can use the following formula to find the production in the first year:

let n be the number of years from the 1st year

(1180-700)/11 = n

n = 48

1st year production = 700-48*10 = 340

So the company's production of excavators in the first year is 340 (Option b)

ii) To find the company's production in the 6th year, we can use the same formula:

6th year production = $700-48*5 = 460$

So the company's production in the 6th year is 460 (Option d)

iii) To find the total production of excavators in the first 8 years, we can use the formula for the sum of an arithmetic series:

$S_n = n/2*(2a+(n-1)d)$

where $S_n$ is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

n = 8

a = 340

d = 48

$S_8 = 8/2*(2340+(8-1)48) = 8(680+280) = 8960 = 7680$

So the total production of excavators in the first 8 years is 7680 (Option c)

iv) To find the year in which the company's production was 1340 excavators, we can use the fact that the company increased its production uniformly by a fixed number every year. Since the company's production in the first year was 340 and the common difference is 48, we can use the following formula:

$1340 = 340 + (year-1)*48$

$year = (1340-340)/48 + 1 = 9$

So the company's production was 1340 excavators in the 9th year.

v) To find the sum of the last ten terms of the AP 8,10,12,...,126, we can use the formula for the sum of an arithmetic series:

$S_n = n/2*(2a+(n-1)d)$

where$S_n$ is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

n = 10

a = 108

d = 2

$S_10 = 10/2*(2108+(10-1)2) = 10(216+18) = 10234 = 2340$

So the sum of the last ten terms of the AP 8,10,12,...,126 is 2340 (Option a)

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Answer 2

Answer:

Step-by-step explanation: