Let the total amount be 3x Case 1: Smaller amount =x, rate of interest =10 Larger amount =2x, rate of interest =5 Total amount received at the end of two years (smaller amount)=x(1+
10
100
)2=1.21x.CI=0.21x Total amount received at the end of two years (larger amount) 2x(1+
5
100
)2=2.205x.CI=0.205x Given, 0.21x+0.205x=830 ⇒x=2000 2x=4000 Case 2:Smaller amount =x, rate of interest =20 Larger amount =2x, rate of interest =10 Total amount received at the end of two years( smaller amount) x(1+
20
100
)2=1.44x.CI=0.44x Total amount received at the end of two years( larger amount) 2x(1+
10
100
)2=2.42x.CI=0.42x Given, 0.44x+0.42x=830 ⇒x=965.11 which is not valid since it should be greater than 1000.