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% ?

Let the amount Vijay invested at the rate of 10% = Rs x
The amount invested at 15% = Rs (50,000 – x)
Time = 1yr
Income from 10% rate = 10% of x = x/10
Income from 15% rate = 15% of (50,000 – x) = (150,000 – 3x)/20

According to question,
[x/10] + [(150,000 – 3x)/20] = 7000
150000 – x = 140000
x = 10,000.
Therefore, he has invested Rs 10,000 at 10% and Rs 40,000 at 15%.