let assume investment amount be 100 , first year interest =100*10%=10, second year (100+10)*10%=11, third year (100+10+11)=121*10%=12.1 hence 10+12.1=2652 , first year interest= 2652/(10+12.1)*10=1200,cost of investment(sum)=1200/10% (or) 0.1=12000

ex :-

Let the sum of money be Rs 100

Rate of interest= 10% p.a.

Interest at the end of 1st year= 10% of Rs100= Rs10

Amount at the end of 1st year= Rs100 + Rs10= Rs110

Interest at the end of 2nd year=10% of Rs110 = Rs11

Amount at the end of 2nd year= Rs110 + Rs11= Rs121

Interest at the end of 3rd year=10% of Rs121= Rs12.10

Difference between interest of 3rd year and 1st year

=Rs12.10- Rs10=Rs2.10

When difference is Rs2.10, principal is Rs100

When difference is Rs252, principal =

[tex] \frac{100 \: \times \: 252}{2.10} [/tex]

=Rs12,000 Ans.

Incorrect question,

The correct question is given bellow;-

A certain sum of money invested at the rate of 10 percent per annum compounded annually, the interest for the first year plus the interest for the third year is Rs. 2,652. Find the sum.

Let consider the sum of money will be Rs.x

Rate of interest per annum=10%    ( given)

Amount=P (1+[tex]\frac{R}{100}[/tex]​)ⁿ          ( P = principal, R = rate of interest, n = number of year)

Let,s calculate for the first year

Amount=x(1+ [tex]\frac{10}{100}[/tex]) ¹

            =  [tex]\frac{11x}{10}[/tex]

Interest=( [tex]\frac{11x}{10}[/tex] −x)

          = [tex]\frac{x}{10}[/tex]

For the second year

P=Rs. [tex]\frac{11x}{10}[/tex]

Amount=[[tex]\frac{11x}{10}[/tex] (1+ [tex]\frac{10}{100}[/tex]​)]= [tex]\frac{121x}{100}[/tex]

For the third year

P=Rs [tex]\frac{121x}{100}[/tex]

Amount= [[tex]\frac{121x}{100}[/tex] ​(1+[tex]\frac{10}{100}[/tex] ​)]= [tex]\frac{1331x}{1000}[/tex]

Interest=( [tex]\frac{1331x}{1000}[/tex]  - [tex]\frac{121x}{100}[/tex]) = [tex]\frac{121x}{1000}[/tex]

According to the sum,

(the interest for the first year + interest for the third year)=Rs.2652

∴( [tex]\frac{1x}{10}[/tex]  + [tex]\frac{121x}{1000}[/tex])=2652

⇒0.221x=2652

⇒x= [tex]\frac{2652}{0.221}[/tex]

⇒x=12000

Hence the sum will be Rs.12000

Ans:- The sum will be Rs.12000.

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