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rs 24000 are lent out for 2 years at compound interest. the rate of interest being 10% for the first year and 12% for the second year .the borrower returns some money at the end of 1st year and on paying rs 12768 at the end of second year ,the total debit is cleared. calculate the amount of money return at the end of first year.(without formula)

Principal for first year, P1 = Rs 24000Rate for first year, R1 = 10% p.a.Tme, T1 = 1 yrI1 = P1R1T1100 = 24000×10×1100 = Rs 2400A1 =P1 + I1 = 24000 + 2400 = Rs 26400Let the amount of money returned at the end of first year = Rs xPrincipal for second year, P2 = Rs 26400-xRate for second year, R2 = 12% p.a.Time, T2 = 1 yrI2 = P2R2T2100 = 26400-x×12×1100 Now, A2 = P2+I2 = 26400-x + 26400-x12100 = 26400-x1 + 325 = Rs282526400-xBut 26400-x2825 = 12768⇒26400-x = 12768×2528 = 11400⇒x = 26400-11400 = 15000amount of money returned at the end of first year = Rs 15000

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p=rs 2400

r=10%",12%

t=2yrs

for 1st year

p=2400

r=10%

t=1yr

I=2400 X 10 X 1

  100

=2400

let  money returned at the end of first year be  x

A=(24000+2400)-x

  =26400 - x

for 2nd year

p=26400-x

r= 12%

t=1yr

I= (26400-x) X 12 X 1

  100

  = 316800-12x

  100

  A = (26400-x)+ 316800-12x

  100

  =100(26400-x)+12(26400-x)

  100

 money returned at the end of first year= 

  100(26400-x)+12 (26400-x)  =  12768

  100

  112(26400-x)  =  12768

  100

  26400-x  =12768 X 100

  112

  26400-x  =11400

  26400-11400 =  x

  15000  =x

money returned at the end of firs year  =15000

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