Quantitative Aptitude Ques 229

Question: A sum of money lent out at compound interest increases in value by 50% in 5 yr. A person wants to lend three different sums x, y and z for 10, 15 and 20 yr, respectively at the above rate in such, a way that he gets back equal sums at the end of their respective periods. The ratio x : y : z is

Options:

A) 6: 9: 4

B) 9: 4: 6

C) 9: 6: 4

D) 6: 4: 9

Show Answer

Answer:

Correct Answer: C

Solution:

  • Compound interest $ =x{{( 1+\frac{50}{100} )}^{10}}=y{{( 1+\frac{50}{100} )}^{15}}=z{{( 1+\frac{50}{100} )}^{20}} $ According to the question, $ {{( \frac{3}{2} )}^{2}}x={{( \frac{3}{2} )}^{3}}y={{( \frac{3}{2} )}^{4}}z=klet $

$ \Rightarrow $ $ x={{( \frac{2}{3} )}^{2}}k, $ $ y={{( \frac{2}{3} )}^{3}}k $ and $ z={{( \frac{2}{3} )}^{4}}k $

$ \therefore $ $ x:y:z={{( \frac{2}{3} )}^{2}}k:{{( \frac{2}{3} )}^{3}}k:{{( \frac{2}{3} )}^{4}}k $ $ =1:\frac{2}{3}:{{( \frac{2}{3} )}^{2}}=9:6:4 $

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