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The simple interest and compound interest of a certain sum of mone for 2 years are Rs. 840 and Rs. 869.40 respectively. Find the sum of money and the rate of interest.

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Let the principal be Rs.`x` and the rate of interest be r%
Then the simple interest of Rs. X in 2 years `=(x xxrxx2)/100`
As per question `(2xr)/100=840`
`implies(xr)/100=420`………..1
Again the compound interest of Rs. x in 2 years
`=Rs.{x xx(1+r/100)^(2-x)}`
`=Rs.x xx{(1+r/100)^(2)-(1)^(2)}`
`=Rs. x xx(1+r/100+1)(1+r/100-1)`
`=Rs. xxx(2+r/100)xxr/100`
`=Rs.(xr)/100(2+r/100)`
`=Rs.420(2+r/100)[ :' "by"(1),(xr)/100=420]`
As per questiino `420(2+r/100)=869.40`
or `2+r/100=869.40/420`
or `(200+r)/100=86940/(420xx100)`
or `200+r=86940/420`
or `200+r=207`
or `r=207-200` or `r=7`
`:.` From 1 we get `(x xx7)/100=420`
or `x=(420xx100)/7=6000`
Hence the sum of money `=Rs. 6000` and the rate of interest per annum is 7%.
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