The ratio of the total compound interest of x% per year earned in firs

Question

The ratio of the total compound interest of x% per year earned in firsts two years to the total simple interest of x% per year earned in first two years on the same amount is 11 : 10. What is the value of x?

A. 10%
B. 20%
C. 25%
D. 30%
E. 40%

A. 10%
B. 20%
C. 25%
D. 30%
E. 40%

rajatchopra1994 · Answer

Explanation:
Checking by Options:

Let Interest is 20%
let Principal is 100, T= 2 Years, R = 20
S.I = 40
C.I = 44

C.I/S.I = 44/40 = 11/10 
IMO-B

SaikatRoy · Answer

Given CI/SI = 11/ 10
Now, CI= Amount in two years - Principal
or CI= P(1+ X/100) ^2 - P
And SI when time is 2 years is
SI= 2PX/100

Also as
CI = 2PX/100+ PX^2/1000
Hence
CI/SI= 1 + X/2

And its given that
CI/SI= 11/10
or 1+ X/2 = 11/10
or 10+5X=11
X= 1/5= 0.20 or 20%

Answer is Option (B)

TestPrepUnlimited · Answer

Set the interest rate as x. The compound interest rate formula is  X = P * (1 + x)^t  where P is the principal, t is number of years. Let us set P = 1 since we are given ratios to work with. Then for two years we earn  X = x^2 + 2x + 1  in total, however P = 1 is the principal so the actual interest accrued on top of the principal, over two years, is  x^2 + 2x . On the other hand for simple interest rate (and P = 1), the interest is 2x. Then we have 
 (x^2 + 2x) / 2x = 11/10  
 x^2 + 2x = 2.2x 
 x^2 - 0.2x = 0 
 x ( x - 0.2) = 0 
 x = 0.2

Ans: B

SaquibHGMATWhiz · Answer

Solution:

Given  \frac{CI}{SI=}\frac{11}{10}

⇒\frac{p }{\frac{P	imes x	imes 2}{100}}=\frac{11}{10}

⇒\frac{(\frac{100+x}{100})^2-1}{\frac{2x}{100}}=\frac{11}{10}

⇒\frac{\frac{(100+x)^2-10000}{100}}{2x}=\frac{11}{10}

⇒\frac{(100+x)^2-10000}{200x}=\frac{11}{10}

⇒10000+x^2+200x-10000=220x

⇒x^2=20x

⇒x=20  (cancelling x both sides because we know x cannot be 0)

Hence the right answer is    Option B

KarishmaB · Answer

The only difference between the SI of two years and CI of two years is the interest earned on first year interest in the case of CI. If $10 is the interest earned in two years on SI, it means $5 was earned as interest each year. In case of CI, it is $11, a $1 extra because this was the interest earned on $5 - the interest of previous year. Since 1/5 is 20% the rate of interest, x%, must be 20%. Answer (B) Check this video for diff between CI in consecutive years: https://youtu.be/pfjZE2xcf04 and try out this question: https://anaprep.com/arithmetic-solving- ... -interest/

The ratio of the total compound interest of x% per year earned in firs

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