Question

A manufacturer of wire produced 1400 metres wire in the 5th year and 1600 metres in the 9th year. Assuming that the production increases uniformly by a fixed number every year, find
1) the production in the 12th year
2) in which year the production will be 1900 m?
3) the total production in 9 years.

Answers: 1) 1750m; 2) 15th year; 3) 12600m

​Please provide the solution

Answer 1

Answer:

Step-by-step explanation:

a5=a+4d

1400=a+4d. (1)

a9=a+8d

1600=a+4d. (2)

Subtracting eq 2 n 1

1600=a+8d

-1400=-a-4d

200=4d

D=50

a+400=1600 (frm eq 2)

a=1200

a12=a+11d

1200=11*50

1200+550

1750 is the ans

Answer 2

1) Production in 12 th year = 1750 m

2) At 15th year the production will be 1900 m

3) Total production in 9 years = 12600 m

Given:

A manufacturer of wire produced 1400 m in 5th year

1600 meters of wire in 9th year

The production increases uniformly by fixed number for every year

To find:

1) the production in the 12th year

2) in which year the production will be 1900 m?

3) the total production in 9 years

Solution:

Let a be the length of the wire produced in 1st year and d be uniform increment in production, then the productions of wire for each year will represent a Arithmetic Sequence

As we know nth term in Ap = a + (n-1) [ production in nth year ]

5th term of AP = a + (5-1)d          [ production in 5th year ]

⇒ a + 4d = 1400_ (1)                 [ from data ]

9th term of AP = a + (9-1)d            

⇒ a + 8d = 1600 _ (2)  

Subtract (1) from (2)

⇒ a + 8d - a - 4d = 1600 - 1400

⇒  4d = 200

⇒ d = 50

The uniform increase for each year is 50 meters

substitute d = 50 in (1)

⇒  a + 4(50) = 1400

⇒ a = 1400 - 200 = 1200

The production in 1st year a = 1200 m

1) the production in the 12th year

⇒ 12th term of AP =  1200 + (12-1)50 = 1200 + 550 = 1750 m

Production in 12 th year = 1750 m

2) in which year the production will be 1900 m

⇒ Assume that at nth year the production will be 1900

⇒ nth term, a + (n-1)d = 1900

⇒ 1200 + (n-1) 50 = 1900

⇒ (n-1) 50 = 700

⇒ n-1 = 14

⇒ n = 15 year

At 15th year the production will be 1900 m

3) the total production in 9 years.

As we know n terms in AP = n/2 [2a + (n – 1)d]  

⇒ sum of 9 term = 9/2 [2(1200) + (9 – 1)50]  

= 9/2 [ 2400 + 400 ]

= 9/2 [ 2800 ] = 9(1400) = 12600 m

Total production in 9 years = 12600m

#SPJ5