In how much time simple interest on Rs.5000 at a rate of 12.5% be the same as the simple interest on Rs.6500 at the rate of 6.5% for 3 years?

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Solution

$P_{1} =$ Rs. $5000$ $P_{2} =$ Rs. $6500$
$R_{1} = 12.5 %$ $R_{2} = 6.5 %$
$T_{1} = ?$ $T_{2} = 3$ years
$S I_{1} = \frac{P_{1} \times R_{1} \times T_{1}}{100}$ $S I_{2} = \frac{P_{2} \times R_{2} \times T_{2}}{100}$
$S I_{1} = \frac{5000 \times 12.5 \times T_{1}}{100}$ $S I_{2} = \frac{6500 \times 6.5 \times 3}{100}$
$S I_{1} =$ Rs. $625. T_{1}$ $S I_{2} =$ Rs. $1267.5$
Since, both the simple interest are to equal themselves.
$∴ 1267.5 = 625 \times T_{1}$
$∴ T_{1} = \frac{1267.5}{625} = 2.02$ years
$∴= T_{1} = 2$ years.

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In how much time simple interest on Rs.5000 at a rate of 12.5% be the same as the simple interest on Rs.6500 at the rate of 6.5% for 3 years?

P1=Rs. 5000 P2=Rs. 6500R1=12.5% R2=6.5%T1=? T2=3 yearsSI1=P1×R1×T1100 SI2=P2×R2×T2100SI1=5000×12.5×T1100 SI2=6500×6.5×3100SI1=Rs. 625.T1 SI2=Rs. 1267.5Since, both the simple interest are to equal themselves.∴1267.5=625×T1∴T1=1267.5625=2.02 years∴=T1=2 years.