Deepa has to buy a scooty. She can buy scooty either by making a cash down payment of ₹ 25,000 or by making 15 monthly installments as below. 1st month -3425, 2nd month-3225, 3rd month -3025, 4th month -2825, and so on. Find the total amount paid in 15 installments.

A
₹ $30375$
B
₹ $20355$
C
₹ $20757$
D
₹ $25252$

Solution:

Given that, Deepa has to buy a scooty. She can buy scooty either making cash down payment of ₹ 25,000 or by making 15 monthly instalments as below.
1st month

- 3425

, 2nd month

- 3225

, 3rd month

- 3025

, 4th month

- 2825,

and so on.
Here the common difference between instalments is,
d = 3225 – 3425
d = -200
If a is the first term, d is the common difference, the sum of the first n terms is given by,

S = \frac{n}{2} (2 a + (n - 1) d)

Let us find the amount paid in 15 installments.
Here, a = 3425
d = -200
n = 15
Calculate the total amount paid in 15 installments.

S = \frac{n}{2} (2 a + (n - 1) d)

\Rightarrow S = \frac{15}{2} (2 \times 3425 + (15 - 1) \times (- 200))

\Rightarrow S = \frac{15}{2} (6850 - 2800)

\Rightarrow S = ₹ 30375

So, the total amount paid by Deepa is ₹30375.
Hence, option (1) is correct.

Deepa has to buy a scooty. She can buy scooty either by making a cash down payment of ₹ 25,000 or by making 15 monthly installments as below. 1st month $- 3425$ , 2nd month $- 3225$ , 3rd month $- 3025$ , 4th month $- 2825,$ and so on. Find the total amount paid in $15$ installments.

Solution:

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