Question

the production of TV sets in a factory increases uniformly by a fixed number every years . if produced $8000$ sets in 6th years, and $11300$ in 9th years. Find the production in (i) first year (ii) 8th year (iii) 6 years

Answer 1

Say TV sets in a factory increases uniformly by a fixed number $d$ every years. Production of first year is $a$.

Since the whole scenario satisfies the conditions of $ArithmeticProgression$

Then

Production of $6^{th}$ years $=a+5d$

$a+5d=8000$ ......(1)

Production of $9^{th}$ years $=a+5d$

$a+8d=11300$ ......(2)

Subtracting equation (1) from (2), We get

$3d=3300$

$d=1100$

Substituting the value of $d$ in equation (1), we get

$a+5500=8000$

$a=2500$

TV sets in a factory increases uniformly by a fixed number $d=1100$ every years. Production of first year is $a=2500$.

$ii)$Production of $8^{th}$ year $=2500+7\times 1100=10200.$