A person borrowed Rs.500 @ 3% per annum S.I. and Rs.600 @ 4.5% per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.126. The number of years, after which the borrowed sum is to be returned, is:
Interest=PRT/100, I(1) =500*3/100*1 =15 I(2)=600*4.5/100*1 =27,since we are looking for T=time I(r)= 15 per annum I(2)=27 per annum (I(1) +I(2))=15+27=42 in 2 annums, if 2 annums=42,then how many annums for 126(total interest),assume time =a,then,if 2y=42,a=126,cross multiple=42a=2(126),a=252/42=6,then if T[1]+T[2]=6,then 2T=6,T=3 T=3
To find the number of years after which the borrowed sum is to be returned, we can use the formula for Simple Interest:
Simple Interest (SI) = (Principal * Rate * Time) / 100
Let's calculate the interests earned on both amounts separately:
Interest on Rs.500 at 3% per annum:
Interest_1 = (500 * 3 * Time_1) / 100
Interest on Rs.600 at 4.5% per annum:
Interest_2 = (600 * 4.5 * Time_2) / 100
According to the problem, the total interest earned should be Rs.126:
Interest_1 + Interest_2 = 126
Substituting the above expressions for Interest_1 and Interest_2, we get:
(500 * 3 * Time_1) / 100 + (600 * 4.5 * Time_2) / 100 = 126
Simplifying the equation:
(15 * Time_1) + (27 * Time_2) = 126
Now we need to find the values of Time_1 and Time_2, which represent the number of years.
If we assume that Time_1 and Time_2 are integers, let's check for multiples of 126 satisfying the equation:
15 * Time_1 + 27 * Time_2 = 126
Multiples of 126:
1 * 126 = 126
2 * 126 = 252
3 * 126 = 378
4 * 126 = 504
By trying these multiples in the equation, we can see that:
Time_1 = 4 and Time_2 = 2 satisfies the equation:
15 * 4 + 27 * 2 = 126
Therefore, the borrowed sum will be returned after 4 + 2 = 6 years.
To find the number of years after which the borrowed sum is to be returned, we need to calculate the total interest earned on each of the loans and then find the total time required for the combined interest to reach Rs. 126.
Let's calculate the interest on each loan separately:
For the loan of Rs. 500 at 3% per annum:
Simple Interest = (Principal * Rate * Time) / 100
SI1 = (500 * 3 * T1) / 100
For the loan of Rs. 600 at 4.5% per annum:
SI2 = (600 * 4.5 * T2) / 100
According to the problem, the total interest earned from both loans is Rs. 126. So, we can write the equation:
SI1 + SI2 = 126
Let's substitute the values in the equation and solve for T1 (time for the first loan) and T2 (time for the second loan):
(500 * 3 * T1) / 100 + (600 * 4.5 * T2) / 100 = 126
15T1 + 27T2 = 126
We need to find the values of T1 and T2 that satisfy the equation. We can use trial and error to find the solution. Let's consider some possible values for T1 and T2:
T1 = 2 years, T2 = 4 years:
15(2) + 27(4) = 30 + 108 = 138 (Not equal to 126)
T1 = 3 years, T2 = 2 years:
15(3) + 27(2) = 45 + 54 = 99 (Not equal to 126)
T1 = 4 years, T2 = 1 year:
15(4) + 27(1) = 60 + 27 = 87 (Not equal to 126)
T1 = 5 years, T2 = 0 years:
15(5) + 27(0) = 75 + 0 = 75 (Not equal to 126)
From the given possible values, none of them satisfy the equation. Hence, it seems there is no solution for the given problem.