A sum of money is invested for 3 years at a particular rate of interest. If the rate of interest were 3% p.a. higher, the interest would have been Rs 1467 more. Find the sum of money.

Asked by Sujitkumarm | 4th Jul, 2020, 09:38: PM

Expert Answer:

Let the sum be P and rate of interest be R.

Therefore, Interest = PNR/100
 
straight I equals fraction numerator straight P cross times 3 cross times straight R over denominator 100 end fraction equals fraction numerator 3 PR over denominator 100 end fraction
If space rate space of space interest space is space straight R plus 3 comma space the space interest space would space be space straight I plus 1467
rightwards double arrow straight I plus 1467 equals fraction numerator 3 straight P left parenthesis straight R plus 3 right parenthesis over denominator 100 end fraction
rightwards double arrow straight I equals fraction numerator 3 straight P left parenthesis straight R plus 3 right parenthesis over denominator 100 end fraction minus 1467
rightwards double arrow fraction numerator 3 PR over denominator 100 end fraction equals fraction numerator 3 straight P left parenthesis straight R plus 3 right parenthesis over denominator 100 end fraction minus 1467
rightwards double arrow 1467 equals fraction numerator 3 straight P left parenthesis straight R plus 3 right parenthesis over denominator 100 end fraction minus fraction numerator 3 PR over denominator 100 end fraction equals fraction numerator 3 PR plus 9 straight P minus 3 PR over denominator 100 end fraction
rightwards double arrow fraction numerator 9 straight P over denominator 100 end fraction equals 1467
rightwards double arrow straight P equals fraction numerator 1467 cross times 100 over denominator 9 end fraction equals 163 cross times 100 equals 16300
Hence comma space the space sum space of space money space is space Rs. space 16300

Answered by Renu Varma | 6th Jul, 2020, 12:14: PM