A number theory problem by A Former Brilliant Member

Number Theory Level 1

Condition 1:On a certain principle, the interest earned for 7 years is $98. Condition 2:On a certain principle, the interest earned for three and a half year is $490 What is the ratio of both the principles?

Details and assumptions:- The ratio must be Condition 2: Condition 1. If your answer is 2:3, write your answer as 2.3


The answer is 10.1.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

The details and assumptions provided made it all clear.

Condition 2 : Condition 1 3.5/490 : 7/98

= 10 : 1

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Anubhav Sharma
Apr 10, 2014

Let's solve it according to the condition

Condition 1

I = \­( \frac{PTR}{100}\­)

or, P = \­( \frac{100 * I }{TR}\­)

or, P = \­( \frac{100 * 98 }{7 years * R}\­)

or, P = \­( \frac{1400 }{ R}\­)

Condition 2

I = \­( \frac{PTR}{100}\­)

or, P = \­( \frac{100 * I }{TR}\­)

or, P = \­( \frac{100 * 490 }{3.5 years * R}\­)

or, P = \­( \frac{14000 }{R}\­)

Now, taking ratios,

( NOTE : The ratio is Condition 2 to Condition 1.)

So, Condition 2 : Condition 1

= \­( \frac{14000 }{ R}\­) : \­( \frac{1400 }{R}\­)

= 14000 : 1400

= 10 : 1

Since, we need to specify the answer in decimal as mentioned in the question. It is 10.1

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