The production of TV sets in a factory increases uniformly by a fixed number every year . It produced 16000 sets in 6th year and 22600 in 9th year.
1. Find the production in first year.
2.Find the production in 8th year.
3. Find the production during first 3 years.
4. In which year, the production is Rs. 29,200.
Step-by-step explanation:
Solution :
Let the production during first year be a and let d be the increase in production every year. Then,
T6=16000⇒a+5d=16000…(i)
andT9=22600⇒a+8d=22600…(ii)
On subtracting (i) from (ii), we get
3d=6600⇒d=2200
Putting d = 2200 in (i), we get
a+5×2200=16000⇒a+11000=16000
⇒a=16000-11000=5000
Thus, a = 5000 and d = 2200.
(i) Production during first year, a = 5000
(ii) Production during 8th year is given by
T8=(a+7d)=(5000+7×2200)=(5000+15400)=20400.
(iii) Production during first 6 years is given by
S6=
6
2
{2a+5d}=3(2×5000+5×2200)
=3(10000+11000)=63000