Question

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Answer 1

It is given that Shamshad Ali bought a scooter for Rs 22000. He paid Rs 4000 in cash.

Let the unpaid amount be U.

The unpaid amount is given by,

U=22000−4000 =18000 Rs

According to the given condition, the interest paid annually is 10%.

The obtained sum S of total interest paid is given by,

S=0.1×18000+0.1×17000+0.1×16000+…+0.1×1000 =0.1×1000+0.1×2000+0.1×3000+…+0.1×18000 =0.1( 1000+2000+…18000 ) (1)

The sequence 1000,2000,…18000 forms an A.P.

Let a and d be the first term and common difference of the given A.P.

Here,

a=1000 d=1000

The formula for the n th term of an A.P. is given by,

a n =a+( n−1 )d

Substitute the corresponding values in the above expression.

18000=1000+( n−1 )( 1000 ) 18000−1000=1000n−1000 17000+1000=1000n 18000=1000n

Further simplify the above expression.

n= 18000 1000 =18

The formula for sum of n terms in an A.P. is given by,

S n = n 2 [ 2a+( n−1 )d ](2)

Substitute the values in equation (2) to find the sum of 18 terms of the given sequence.

S 18 = 18 2 [ 2( 1000 )+( 18−1 )( 1000 ) ] =9[ 2000+17×1000 ] =9[ 2000+17000 ] =9×19000 (3)

Substitute the value of equation (3) in equation (1).

S=0.1( 1000+2000+…18000 ) =0.1( 9×19000 ) =0.1×171000 =17100

The total interest paid is 17100.

The net cost C of the scooter is given by,

C=22000+17100 =39100 Rs

Thus, the total cost of the scooter is Rs. 39100.