Question

2. A part of ₹ 1500 was lent at 10% per annum and the rest at 7% per annum simple interest. The total
interest earned in 3 years was ₹396. What was the sum lent at 10% p.a?

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Answer 1

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▪ A part of Rs. 1500 was lent at 10% per annum and the rest at 7% per simple interest.
The total interest earned in 3 years was Rs. 396. what was the sum lent at 10% p.a. ??




${ \red{ \underline{ \underline{ \huge{ \rm{S}}{ \mathfrak{olution}}}}}}$




▪ Total money invested = Rs. 1500



Let the first part be Rs. x , then the other part will be Rs. ( 1500-x )



${ \green{ \sf{ \underline{first \: part}}}}$



• Principal ( P ) = Rs . x


• Rate ( R ) = 10 %


• Time ( T ) = 3 years


S.I. = (P * R * T) /100



➞ S.I. = (x * 10 * 3)/100



➞ S.I. = Rs. 30x/100



${ \sf{\green{ \underline{second \: part}}}}$



• Principal ( P ) = Rs. ( 1500 - x )



• Rate ( R ) = 7%



• Time ( T ) = 3 years



S.I. = ( P * R * T )/100



➞ S.I. = ( 1500-x ) * 7 * 3 / 100



➞ S.I. = Rs. ( 1500 - x )21 / 100



▪ Total interest earned = Rs. 396



${ \sf{ \frac{30x}{100} + \frac{(1500 - x)21}{100} = 396}}$



${ \sf{ \implies{ \frac{30x + (1500 \times 21) - 21x}{100} = 396}}}$



${ \implies{ \sf{9x + 31500 = 396 \times 100}}}$



${ \sf{ \implies{9x = 39600 - 31500}}}$



${ \implies{ \sf{9x = 8100}}}$



${ \implies{ \sf{x = Rs . \: 900}}}$



therefore,


money lent at 10% per annum is equal to Rs. 900