Sequence And Series Question 47
Question: Jairam purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installment of Rs. 1000 with 10% per annum interest. How much money is to be paid by Jairam
[UPSEAT 1999]
Options:
A) Rs. 21555
B) Rs. 20475
C) Rs. 20500
D) Rs. 20700
Show Answer
Answer:
Correct Answer: C
Solution:
It will take 10 years for Jairam to pay off Rs. 10000 in 10 yearly installments. $ \because $ He pays 10% annual interest on remaining amount
$ \therefore $ Money given in first year $ =1000+\frac{10000\times 10}{100}=Rs.2000 $ Money given in second year = 1000 + interest of (10000 - 1000) with interest rate 10% per annum $ =1000+\frac{9000\times 10}{100}=Rs.,1900 $ Money paid in third year = Rs. 1800 etc. So money given by Jairam in 10 years will be Rs. 2000, Rs. 1900, Rs. 1800, Rs. 1700,…., which is in arithmetic progression, whose first term $ a=2000 $ and $ d=-100 $ Total money given in 10 years = sum of 10 terms of arithmetic progression $ =\frac{10}{2}[2(2000)+(10-1)(-100)] $ = Rs. 15500 Therefore, total money given by Jairam $ =15500=Rs\text{. },15500\text{.} $
BETA
