Mr. X invested a part of his investment in 10% bond A and a part in 15% bond B. His interest income during the first year is Rs.4,000. If he invests 20% more in10% bond A and 10 % more in 15% bond B, his income during the second year increases by Rs.500. His initial investment and the new investment in bonds A and B are
To solve this problem, we need to use a system of equations and solve simultaneously.
Let's assume that Mr. X initially invested x rupees in bond A and y rupees in bond B.
According to the given information, Mr. X's interest income during the first year is Rs. 4,000.
Therefore, using the formula for interest:
Total interest income from bond A = (x * 10%) = 0.1x
Total interest income from bond B = (y * 15%) = 0.15y
The total interest income during the first year is the sum of the interest income from bond A and bond B:
0.1x + 0.15y = 4000 ...........(Equation 1)
According to the second condition, Mr. X invested 20% more in bond A and 10% more in bond B.
Hence, his new investment in bond A = x + 0.2x = 1.2x
His new investment in bond B = y + 0.1y = 1.1y
According to the given information, Mr. X's income during the second year increased by Rs. 500.
Therefore, the new total interest income from bond A = (1.2x * 10%) = 0.12x
The new total interest income from bond B = (1.1y * 15%) = 0.165y
The new total interest income during the second year is the sum of the interest income from bond A and bond B:
0.12x + 0.165y = 4500 ...........(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and y). We can solve this system to find the values of x and y.
Solving equations 1 and 2 simultaneously will give us the values of x and y, which represent Mr. X's initial investment and new investment in bonds A and B.
.10x + .15y = 4000
.10(1.2x) + .15(1.1y) = 4000+500
220
If the amounts in A and B are x and y, then
.10x + .15y = 4000
.10(1.2x) + .15(1.1y) = 4000+500