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A sum of money is lent at simple interest and compound interest. The ratio between the difference of compound interest and simple interest of 3 years and 2 years is 35 : 11. What is the rate of interest per annum?
  • a)
    20 3/4%
  • b)
    17 2/5%
  • c)
    18 2/11%
  • d)
    22 1/5%
  • e)
    24 5/6%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A sum of money is lent at simple interest and compound interest. The r...
Difference in 3 yrs = Pr2 (300+r)/1003 
Difference in 2 yrs = Pr2 /1002
So Pr2 (300+r)/1003 / Pr2 /1002 = 35/11 (300+r)/100 = 35/11
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A sum of money is lent at simple interest and compound interest. The r...
Given: Ratio of difference of compound interest and simple interest of 3 years and 2 years is 35:11

Let the principal be P and the rate of interest be R% per annum

Formula for Simple Interest (SI) = (P*R*T)/100
Formula for Compound Interest (CI) = P*(1+R/100)^T - P

Difference between CI and SI for 3 years = CI - SI = P*(1+R/100)^3 - P*R*3/100
Difference between CI and SI for 2 years = CI - SI = P*(1+R/100)^2 - P*R*2/100

According to the problem, the ratio of the above two differences is 35:11

(P*(1+R/100)^3 - P*R*3/100)/(P*(1+R/100)^2 - P*R*2/100) = 35/11

Simplifying the above equation, we get:

35(1+R/100) = 33

R = (33/35)*100 = 94.29/3

R = 31.43%

Therefore, the rate of interest per annum is 31.43%, which is equivalent to 18 2/11% (option C) when simplified.
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Community Answer
A sum of money is lent at simple interest and compound interest. The r...
Difference in 3 yrs = Pr2 (300+r)/1003 
Difference in 2 yrs = Pr2 /1002
So Pr2 (300+r)/1003 / Pr2 /1002 = 35/11 (300+r)/100 = 35/11
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A sum of money is lent at simple interest and compound interest. The ratio between the difference of compound interest and simple interest of 3 years and 2 years is 35 : 11. What is the rate of interest per annum?a)20 3/4%b)17 2/5%c)18 2/11%d)22 1/5%e)24 5/6%Correct answer is option 'C'. Can you explain this answer?
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