| 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 |
A) 6: 9: 4
B) 9: 4: 6
C) 9: 6: 4
D) 6: 4: 9
Correct Answer: C
Solution :
| Compound interest |
| \[=x{{\left( 1+\frac{50}{100} \right)}^{10}}=y{{\left( 1+\frac{50}{100} \right)}^{15}}=z{{\left( 1+\frac{50}{100} \right)}^{20}}\] |
| According to the question, |
| \[{{\left( \frac{3}{2} \right)}^{2}}x={{\left( \frac{3}{2} \right)}^{3}}y={{\left( \frac{3}{2} \right)}^{4}}z=k\,\,let\] |
| \[\Rightarrow \] \[x={{\left( \frac{2}{3} \right)}^{2}}k,\]\[y={{\left( \frac{2}{3} \right)}^{3}}k\]and \[z={{\left( \frac{2}{3} \right)}^{4}}k\] |
| \[\therefore \] \[x:y:z={{\left( \frac{2}{3} \right)}^{2}}k:{{\left( \frac{2}{3} \right)}^{3}}k:{{\left( \frac{2}{3} \right)}^{4}}k\] |
| \[=1:\frac{2}{3}:{{\left( \frac{2}{3} \right)}^{2}}=9:6:4\] |
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