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What's Your Question?
Answer

Let x % annual interest rate,

interest on 3000 for one yr is 30x

and interest on 4200 for 8 month is 8*42*2x/12 = 56x

so (30x+56x) = 832 

therefore x = 832/86 = 9.6744 which is near about 9.67%  

Answer

Interest at i% is to be paid for the sum of Rs 3000 for the full year and at 2i% for Rs 4200 for 8 months or 2/3 of the year

So  3000 x i/100 + 4200 x 2i/100 x 2/3 = 832

Or 30i + 56i = 832

Or i = 832/86 = 9.67%

Answer
Rate of interest. - 416/43%
Answer

interest = (principal * rate * time(in years))/100

Let rate of interest in first case is r. 

So interest on 3000 for 1 year = (3000*r*1)/100 = 30r

Now in second case time is 8 months and rate of interest is 2r. 

So interest on 4200 for 8 months (8/12 years) = (4200*2r*8/12)/100 = 56r

Sum of interest = 832

30r+56r = 832

86r = 832

r = 832/86

Answer

For the sum Rs 3000 with rate of interest r the interest for one year is (3000 x 1x r)/100 = 30 r

For the sum Rs 4200 with rate of interest 2r the interest for 8 months is (4200 x 8/12 x 2r)/100 = 56 r

Total interest = 30 r + 56 r = 86 r = 832 => r = 832 / 86 = 9.6744

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