Quantitative Aptitude Ques 2331
Question: A sum of money was invested for 14 yr in scheme A which offers simple interest at a rate of 8% per annum. The amount received from scheme A after 14 yr was then invested for 2 yr in scheme B which offers compound interest (compounded annually) at a rate of 10% per annum. If the interest received from scheme B was Rs. 6678, what was the sum invested in scheme A? [IBPS RRB (Office Assistant) 2015]
Options:
A) Rs. 15500
B) Rs. 14500
C) Rs. 16000
D) Rs. 12500
E) Rs. 15000
Show Answer
Answer:
Correct Answer: E
Solution:
- Let the principal invested in scheme A.
$ SI=\frac{P\times R\times T}{100} $
$ \Rightarrow $ $ SI=\frac{P\times 14\times 8}{100} $
$ SI=\frac{112,P}{100} $
$ A=P+SI=P+\frac{112P}{100}=\frac{212}{100}P $
On compound interest in scheme B.
$ A=\frac{212P}{100}{{( 1+\frac{10}{100} )}^{2}}=\frac{212P}{100}\times {{( \frac{110}{100} )}^{2}} $
$ =\frac{212P}{100}\times \frac{121}{100}=\frac{25652P}{10000} $
Interest received from scheme B
$ =\frac{25652P}{10000}-\frac{212P}{100A} $
$ =\frac{25652P-21200,P}{10000}=\frac{4452P}{10000} $
But given, $ \frac{4452P}{10000}=6678 $
$ P=\frac{6678\times 10000}{4452}=Rs.15000 $
BETA
