A man invests an amount of Rd.15860 in the name of his 3 sons A,B And ...
Problem Statement:
A man invests an amount of Rd.15860 in the name of his 3 sons A,B And c in such a way that they get the same amount after 2, 3 and 4 years respectively. The rate of interest is 5% then the ratio of amount invested in the name of A,B and C is?
Solution:
Step 1: Find the amount that each son will get after 2, 3 and 4 years respectively.
Let the amount invested by the man be x.
Amount A will get after 2 years = x(1+5/100)^2
Amount B will get after 3 years = x(1+5/100)^3
Amount C will get after 4 years = x(1+5/100)^4
Step 2: Equate the amounts received by each son.
As per the problem statement, the amounts received by each son are equal.
x(1+5/100)^2 = x(1+5/100)^3 = x(1+5/100)^4
Step 3: Simplify the equation and solve for x.
x(1+5/100)^2 = x(1+5/100)^3 = x(1+5/100)^4
(1+5/100)^2 = (1+5/100)^3 = (1+5/100)^4
1+0.1+0.0025 = 1+0.15+0.00375 = 1+0.2+0.005+0.000125
1.1025x = 1.158875x = 1.21550625x
x = 15860/1.47788125 = 10730
Therefore, the amount invested in the name of A, B and C respectively is:
Amount invested in the name of A = x = 10730
Amount invested in the name of B = x(1+5/100) = 11266.50
Amount invested in the name of C = x(1+5/100)^2 = 11852.83
Step 4: Find the ratio of the amount invested in the name of A, B and C.
Ratio of the amount invested in the name of A, B and C = 10730:11266.50:11852.83
= 10730:11266.50:11852.83
= 50.5:53:55.5
Therefore, the ratio of amount invested in the name of A, B and C is 50.5:53:55.5.