Question

Mr Anil takes a loan of Rs 2000
from Mr Tom and agrees to repay
in number of instalments, each
instalment (beginning with the
second) exceeding the previous
one by Rs 10. If the first instalment
is Rs 5, find how many
instalments will be necessary to
wipe out the loan completely?

Answer 1

Step-by-step explanation:

According to the question,

Tthe total amount of debit to be paid in 40 installment = Rs 3600

After 30 installment one-third of his debit is left unpaid. This means that he paid two third of the payment. So,

The amount he paid in 30 installments =

3

2

(3600)

= 2(1200)

= 2400

Let us take the first installment as a and common difference as d.

So, using the formula for the sum of n terms of an A.p,

s

n

=

2

n

[2a+(n−1)d]

Let us find a and d, for 30 installments.

s

30

=

2

30

[2a+(30−1)d]

2400=15[2a+(29)d]

15

2400

=2a+29d

160=2a+29d

a=

2

160−29d

.....(1)

Similarly, we find a and d for 40 installment.

s

40

=

2

40

[2a+(40−1)d]

3600=20(2a+(39)d)

20

3600

=2a+39d

a=

2

180−39d

subtracting (1) from (2), we get

a−a=(

2

180−39d

)−(

2

160−29d

)

0=

2

180−39d−160+29d

.....(2)

0=20−10d

Further solving for d

10d = 20

d=

10

20

d = 2 the value

subtracting the value of d in (1), we get,

a=

2

160−29(2)

=

2

160−58

=

2

102

= Rs 51