A person invest two equal sums, one at simple interest and another at compound interest at same rate for two years. After two years the ratio of amount at compound interest to amount on simple interest is 25:16. Find rate.
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A person invest two equal sums, one at simple interest and another at compound interest at same rate for two years. After two years the ratio of amount at compound interest to amount on simple interest is 25:16. Find rate.
Given :- A person invest two equal sums, one at simple interest and another at compound interest at same rate for two years. After two years the ratio of amount at compound interest to amount on simple interest is 25:16. Find rate. ?
Solution :-
- Let us assume that, Principal invest in both = Rs.P
- Let rate of interest in both = R % per annum.
- Time in both = 2 years.
we know that,
- Amount at SI = P + (P * R * T)/100 = P{1 + (RT/100)}
- Amount in CI = P[1 + (R/100)]^T
given that,
- Amount at CI : Amount at SI = 25 : 16
Putting all values we get,
→ P[1 + (R/100)]² / P{1 + (2R/100)} = 25 / 16
→ [1 + (R/100)]² / {1 + (R/50)} = 25 / 16
→ {(100 + R)²/100²} * 16 = 25{(50 + R)/50}
→ (100 + R)² / 625 = (50 + R) / 2
→ 2(10000 + R² + 200R) = 625(50 + R)
→ 2R² + 400R + 20000 = 31250 + 625R
→ 2R² + 400R - 625R + 20000 - 31250 = 0
→ 2R² - 225R - 11250 = 0
→ 2R² - 300R + 75R - 11250 = 0
→ 2R(R - 150) + 75(R - 150) = 0
→ (R - 150)(2R + 75) = 0
→ R = 150 or, (-75/2)
since , negative value of rate is not possible.
→ R = 150% per annum (Ans.)
Hence, Required rate of interest is 150% per annum.
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