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%? Select the correct option:
A) Rs.40,000
B) Rs.40,000
C) Rs.12,000
D) Rs.20,000
E) None
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 = 7000/50000 * 100   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 = 1/5 * 50,000 = 10,000.   Answer Rs.40,000
<result>B</result>
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%?