Question

A car company manufactures 4,800 cars in its $6^{th}$ year and 5,900 cars in its $8^{th}$ year. Assuming that the number of cars manufactured by the company increases by a fixed number every year, find the total number of cars it manufactured in its first 5 years.

• A. 11,500
• B. 15,750
• C. 20,550
• D. 25,900

Answer 1

The correct option is B 15,750

Given,
car manufactured in 6th year $=4,800$
car manufactured in 8th year $=5,900$
cars manufactured by the company increases by a fixed number (d) every year
If a = Car manufactured in $1^{st}$ year and d = extra car manufactured per year then,
Applying AP on 6th year,
AP = a + (n - 1)d = a + 5d = 4800 ------- (1)
Applying AP on $8^{th}$ year,
AP = a + (n - 1)d = a + 7d = 5900 -------- (2)
(2) - (1) = 2d = 1100
$\Rightarrow$ d = 550
( extra car manufactured per year)
From eq (1)
a = 4800 - 2750 = 2050 ( Car manufactured in $1^{st}$ year)

Then the total number of cars it manufactured in its first 5 years $\left(S_5\right)=\frac{n}{2}(2a+(n-1\left)d\right)=\frac{5}{2}(2\times 2050+(5-1\left)550\right)$
= 15750