Sonali invest money in three different schemes for $6$ years at $10 % p, a$ ., $12 % p . a$ and $15 % p . a$ at simple interest respectively. At the completion of each schema, she gets the same interest. What is the ratio of her investments?

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Solution

$I_{1} = \frac{P_{1} \times r_{1} \times t_{1}}{100} = \frac{P_{1} \times 10 \times 6}{100} = \frac{60 P_{1}}{100} = 0.6 P_{1}$

$I_{2} = \frac{P_{2} \times r_{2} \times t_{2}}{100} = \frac{P_{2} \times 12 \times 6}{100} = \frac{72 P_{2}}{100} = 0.72 P_{2}$

$I_{3} = \frac{P_{3} \times r_{3} \times t_{3}}{100} = \frac{P_{3} \times 15 \times 6}{100} = \frac{90 P_{3}}{100} = 0.9 P_{3}$

$I_{1} = I_{2} = I_{3}$
$⟹ 0.6 P_{1} = 0.72 P_{2} = 0.9 P_{3}$
$⟹ P_{1} : P_{2} : P_{3} = 6 : 5 : 4$
Hence, ratio of investments $= 6 : 5 : 4$

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Sonali invest money in three different schemes for 6 years at 10%p,a., 12%p.a and 15%p.a at simple interest respectively. At the completion of each schema, she gets the same interest. What is the ratio of her investments?

I1=P1×r1×t1100=P1×10×6100=60P1100=0.6P1I2=P2×r2×t2100=P2×12×6100=72P2100=0.72P2I3=P3×r3×t3100=P3×15×6100=90P3100=0.9P3I1=I2=I3⟹0.6P1=0.72P2=0.9P3⟹P1:P2:P3=6:5:4Hence, ratio of investments=6:5:4

Sonali invest money in three different schemes for $6$ years at $10 % p, a$ ., $12 % p . a$ and $15 % p . a$ at simple interest respectively. At the completion of each schema, she gets the same interest. What is the ratio of her investments?