Karthi had RS.5000 with him. he lent a part of 12% per annum simple interest and the remaining at 15% per annum. his total annum income was Rs.700.find the sum lent at12% per annum.
If x at 12%, then
.12x + .15(5000-x) = 700
X=5000/3
= Rs. 1666.67 is the sum lent at
12% p.a.
To find the sum lent at 12% per annum, we can use a two-equation system based on the given information.
Let's assume Karthi lent x rupees at 12% per annum. Therefore, he lent (5000 - x) rupees at 15% per annum.
The interest earned from lending x rupees at 12% per annum can be calculated using the formula:
Interest = (Principal * Rate * Time) / 100
So, the interest earned from lending x rupees at 12% per annum is (x * 12 * 1) / 100 = 12x / 100.
Similarly, the interest earned from lending (5000 - x) rupees at 15% per annum is [(5000 - x) * 15 * 1] / 100 = 15(5000 - x) / 100.
According to the given information, the total income from both loans is Rs. 700, so we have the equation:
(12x / 100) + [15(5000 - x) / 100] = 700.
Let's solve this equation to find x, the sum lent at 12% per annum:
12x + 15(5000 - x) = 70000
12x + 75000 - 15x = 70000
-3x = -5000
x = 5000 / 3
x = 1666.67 (rounded to two decimal places)
Therefore, Karthi lent approximately Rs. 1666.67 at 12% per annum.