A man saves ₹ 135 /- in the first year, ₹ 150 / - in the second year and in this way he increases his savings by ₹ 15 /- every year. In what time will his total savings be ₹ 5550 /- ?

Question

A man saves ₹ 135 /- in the first year, ₹ 150 / - in the second year and in this way he increases his savings by ₹ 15 /- every year. In what time will his total savings be ₹ 5550 /- ? (A) 20 years (B) 25 years (C) 30 years (D) 35 years

Tardigrade Admin · Accepted Answer

Given statement makes an AP series where,

a = ₹135

,

d = ₹15

and

S_{n} = ₹5550

Let total savings be

₹5550

in

n

years
So,

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

5550 = \frac{n}{2} [2 \times 135 + (n - 1) 15]

\Rightarrow 11100 = n [270 + 15 n - 15]

\Rightarrow 15 n^{2} + 255 n - 11100 = 0

\Rightarrow n^{2} + 17 n - 740 = 0

\Rightarrow n^{2} + 37 n - 20 n - 740 = 0

\Rightarrow (n + 37) (n - 20) = 0

n = 20 (∵ n \neq = - 37)

Q. A man saves ₹135/− in the first year, ₹150/ - in the second year and in this way he increases his savings by ₹15/− every year. In what time will his total savings be ₹5550/− ?

20 years

25 years

30 years

35 years

Q. A man saves $₹135/ -$ in the first year, $₹150/$ - in the second year and in this way he increases his savings by $₹15/ -$ every year. In what time will his total savings be $₹5550/ -$ ?