Simple & Compound Interest - Quant - CAT 2009
Question 4 the day:
February 10, 2003
The question for the day is from the topic of Ratio and Proportion.
- Vijay invested Rs.50,000 partly at 10% and partly at 15%.
His total income after a year was Rs.7000. How much did he invest at the rate
of 10%?
| (1) |
Rs.40,000 |
| |
(2) |
Rs.40,000 |
| (3) |
Rs.12,000 |
| |
(4) |
Rs.20,000 |
Correct Answer - (2)
Solution:
The best way to solve this problem is by using the concept
in Mixtures and Alligation.
Vijay earned a total income of Rs.7000 for his investment of
50,000.
Therefore, his average rate of return = 
By rule of alligation, if the value of one of the products
is 10 (cheaper) and the other is 15 (dearer) and if the two are mixed such that the average value
of the mixture is 14 (mean price), then the two products have been mixed in the following
ratio.
The ratio of
Cheaper product : Dearer product
(Dearer product price - mean price) : (Mean price -
cheaper product price)
In our example, the cheaper product is the investment at
10%, the dearer product is the investment at 15% and the mean price is the
average return of 14%.
Therefore, the amount invested @10% interest =  = 10,000.
The CAT Way
The easiest way to solve this problem in CAT is by substituting answers.
Let us take answer choice (1) and see. The answer according to this choice is 40,000.
If he had invested Rs.40,000 at 10%, then he would have invested the balance
10,000 at 15%. The total interest earned by him would then be 10% of 40,000 + 15% of 10,000 = 4000+1500 = 5500.
But, the problem states that the total interest earned
by him was Rs.7000. Hence, choice (1) is not the correct answer. Let us evaluate the next choice.
He invested 10,000 at 10% and therefore, the balance 40,000
at 15%. Hence the interest earned by him will be
10% of 10,000 + 15% of 40,000 = 1000 + 6000 = 7000, which is
what the problem states.
Hence this is the correct answer.
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