Question

Bhiku borrowed some money from Dhanraj to admit his daughter in a reputed Law
School. He agreed to pay the interest-free loan of Rs. 60,000 in a monthly installments,
which increased by a constant amount. After the 20th installment, he found that he has
paid 3/4th of the loan. If the entire loan was cleared this way in 25 installments, find out
the value of the first installment.
(A) Rs. 1560
(B) Rs. 1067
(C) Rs. 1680
(D) Rs. 1987
​

Answer 1

Answer:1680

Step-by-step explanation:

Answer 2

The value of the first installment is Rs. 1680. (c).

Given,

3/4th of the amount is paid in the 20th installment.

The whole amount is paid in the 25th installment.

To Find,

The value of the first installment.

Solution,

Let the value of the first installment be a and the increased constant amount be d.

For the 20th installment,

Sₙ = n/2 [2a + (n - 1)d]

⇒ (3/4) x 60000 = 20/2 [2a + (20 - 1)d]

⇒ 45000 = 10 [2a + 19d]

⇒ 2a + 19d = 4500                                             -------------------------------------(1)

For the 25th installment,

Sₙ = n/2 [2a + (n - 1)d]

⇒ 60000 = 25/2 [2a + (25 - 1)d]

⇒ 2a + 24d = 4800                                            ------------------------------------(2)

Subtracting (1) from (2),

⇒ 2a + 24d - 2a - 19d = 300

⇒ 5d = 300

⇒ d = 60

Putting d in (1),

⇒ 2a + 24x60 = 4800

⇒ 2a = 3360

⇒ a = 1680

Hence, the value of the first installment is Rs. 1680.

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