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Sagot :
Answer:
Rs 42000 and Rs 40000
Step-by-step explanation:
Given that Rs 82000 is divided into two parts.
Let the first part be Rs x which is compounded annually at the interest of 5% per annum for 2 years.
The rate of interest = 5%=0.05
The total amount after 2 years [tex]= x(1+0.05)^{2}\cdots(i)[/tex]
The other part is Rs 82000-x which is compounded annually at the interest of 5% per annum for 3 years.
The total amount after 3 years [tex]= (82000-x)(1+0.05)^{3}\cdots(ii)[/tex]
As both the amounts are equal, so from equation (i) and (ii)
[tex]x(1+0.05)^{2}=(82000-x)(1+0.05)^{3} \\\\x(1.05)^{2}=82000(1.05)^{3} -x(1.05)^{3} \\\\x(1.05^2+1.05^3)=82000\times 1.05^3 \\\\x(2.260125)=94925.25 \\\\x=94925.25/2.260125 \\\\[/tex]
x= 42000
And the other part = 82000-42000 = Rs 40000
Hence, he divides the money as
Rs 42000 at 5% per annum compound interest in 2 years and
Rs 40000 at 5% per annum compound interest in 3 years.
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