A sum of Rs.1100 is lent out in two parts. If the interest on one part at 6% for 4 years is equal to that on another part at 2% for 10 years, then find the sum lent out at 6% and 2%

Asked by nvrithikashree | 4th Dec, 2016, 08:23: AM

Expert Answer:

begin mathsize 18px style Let space the space sum space lent space out space at space 6 percent sign space be space Rs. space straight x.
So comma space the space sum space lent space out space at space 2 percent sign space equals space Rs. space left parenthesis 1100 minus straight x right parenthesis
Interest space on space Rs. space straight x space equals space fraction numerator 6 cross times straight x cross times 4 over denominator 100 end fraction
Interest space on space Rs. space left parenthesis 1100 minus straight x right parenthesis space equals space fraction numerator 2 cross times left parenthesis 1100 minus straight x right parenthesis cross times 10 over denominator 100 end fraction
According space to space the space given space condition comma
fraction numerator 6 cross times straight x cross times 4 over denominator 100 end fraction equals fraction numerator 2 cross times left parenthesis 1100 minus straight x right parenthesis cross times 10 over denominator 100 end fraction
rightwards double arrow 6 cross times straight x cross times 4 equals 2 cross times left parenthesis 1100 minus straight x right parenthesis cross times 10
rightwards double arrow fraction numerator 6 cross times straight x cross times 4 over denominator 2 cross times 10 end fraction equals 1100 minus straight x
rightwards double arrow fraction numerator 3 cross times straight x cross times 2 over denominator 1 cross times 5 end fraction equals 1100 minus straight x
rightwards double arrow fraction numerator 6 straight x over denominator 5 end fraction equals 1100 minus straight x
rightwards double arrow fraction numerator 6 straight x over denominator 5 end fraction plus straight x equals 1100
rightwards double arrow fraction numerator 11 straight x over denominator 5 end fraction equals 1100
rightwards double arrow straight x equals fraction numerator 1100 cross times 5 over denominator 11 end fraction equals 500
Hence comma space the space sum space lent space at space 6 percent sign space is space Rs. space 500 space and space the space sum space lent space at space Rs. space 2 percent sign equals 1100 minus 500 equals Rs. space 600 end style

Answered by Rebecca Fernandes | 4th Dec, 2016, 06:23: PM

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