May 24, 2010

Quantitative Ability Question of the Day

Question:
Jayantilal, a shrewd investor, comes to know of two different investment schemes. Scheme A doubles the money in six years by simple interest at a certain rate. Scheme B doubles the money in six years at a different rate, but by compound interest. To keep his money safe, in case a scheme turns out to be a scam, he takes out the money after every 3 years from one scheme and puts into the other. If he starts with scheme A, in how many years will his money become 4.5 times?
OPTIONS
1) 6
2) 8
3) 9
4) 12

Solution


Scheme A is a simple interest scheme, and doubles the money in 6 years. So in 3 years it will make the money 1.5 times.

Scheme B also doubles the money in 6 years, at compound interest.












So scheme B turns the money into √2 times in 3 years.
So, a combination of scheme A followed by scheme B for 3 years each will turn the money into
1.5x√2 times in 6 years.




Therefore, 2 six year periods will make the money 4.5 times.

So, the money will become 4.5 times in 12 years.
Hence, option 4.



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