Question

A person pays a loan of Rs 975 in monthly
installments, each installment being less than the
former by Rs 5: The amount of first installment is
Rs 100. In how many installments will the entire
amount be paid ? Give reason. ​

Answer 1

Given :-

• Total Loan Borrowed = Rs.975 .
• First Installment = Rs.100
• Each Installment Reduced by = Rs. 5.

Answer :-

The Installements Paid are :- 100, 95, 90, 85, ________

So, we can say That, This is Our AP series.

→ First Term = 100 = a

→ Common Difference = 95 - 100 = (-5) = d

→ Sum of nth Terms of AP = 975 .

→ n = ?

we know That :-

→ Sum of n terms of AP = (n/2)[2a + (n - 1)d]

Putting Values Here, we get :-

→ 975 = (n/2)[2 * 100 + (n - 1)(-5) ]

→ 975*2 = n [200 - 5n + 5 ]

→ 1950 = 205n - 5n²

→ 5n² - 205n + 1950 = 0

→ 5(n² - 41n + 390) = 0

→ n² - 41n + 390 = 0

Splitting The Middle Term Now ::-

→ n² - 26n - 15n + 390 = 0

→ n(n - 26) - 15(n - 26) = 0

→ (n - 15)(n - 26) = 0

Putting Both Equal to Zero now, we get,

→ (n - 15) = 0

→ n = 15.

Or,

→ (n - 26) = 0

→ n = 26.

Now, we have Two value of n , which Satisfy the given Condition .

As No more Data is Given, that we have to Find Smaller value or Not.

we can say That, The Person can Pay the loan in Either in 15 installments or he can pay the loan in 26 Installments.

Answer 2

Answer:

15 or 26.

Step-by-step explanation:

Given:

Total loan = Rs. 975

The amount of each installment decreases Rs.5 from the first.

Amount of first installment = Rs. 100

We can say that, the sequence of Amount from first installment will be 100, 95 , 90 , ....

Here , we observe that the following sequence is in AP.

Here , a (first term) = 100

d (Common difference) = t(n) - t(n-1)

= t(2) - t(1)

= 95 - 100

d = -5.

S(n) = 975

We know that, S(n) = n/2 [2a + (n - 1)d]

975 = n/2 [ 2(100) + (n - 1)(-5)]

975 = n/2 [ 200 - 5n + 5]

975(2) = n (205 - 5n)

1950 = 205n - 5n²

390(5) = 5( 41n - n²)

(5 is being cancelled out)

390 - 41n + n² = 0

n² - 41n + 390 = 0

n² - 15n - 26n + 390 = 0

n (n - 15) -26(n - 15) = 0

(n - 26)(n - 15) = 0

n - 26 = 0

n = 26

n - 15 = 0

n = 15

Hence, The entire amount would be paid in 15 or 26 installments.