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Two persons P and Q lent certain amounts at the same rate of interest

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Two persons P and Q lent certain amounts at the same rate of interest  [#permalink]

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New post 25 May 2020, 19:01
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Two persons P and Q lent certain amounts at the same rate of interest for 2 yr and 3 yr, respectively under compound interest. If their final amounts are in the ratio of 3 : 5, Q' s amount at the end of the first year being Rs 8500 and P earned an interest of Rs 510 for the first year, then find the ratio of their principals.

(A) 33 : 50

(B) 27 : 47

(C) 35 : 61

(D) 22 : 51

(E) 23 : 49
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Re: Two persons P and Q lent certain amounts at the same rate of interest  [#permalink]

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New post 30 May 2020, 19:41
karan12345 wrote:
Two persons P and Q lent certain amounts at the same rate of interest for 2 yr and 3 yr, respectively under compound interest. If their final amounts are in the ratio of 3 : 5, Q' s amount at the end of the first year being Rs 8500 and P earned an interest of Rs 510 for the first year, then find the ratio of their principals.

(A) 33 : 50

(B) 27 : 47

(C) 35 : 61

(D) 22 : 51

(E) 23 : 49


let principal amounts of P & Q be "p" and "q" respectively
let rate be x% compounded annually

interest at the end of 1st year for P
\(\frac{p*x}{100} = 510\) ----- (i)

amount at the end of 1st year for Q
\(q*(1+x/100) = 8500\)----- (ii)

P's amount at the end of 2 yrs/ Q's amount at the end of 3 yrs = \(\frac{3}{5}\)
\(p*(1+x/100)^2 / q*(1+x/100)^3 = 3/5\)------ (iii)
\(p / q*(1+x/100) = 3/5\)
from (ii), we get
\(\frac{p}{8500} = \frac{3}{5}\)
or \(p = 5100\) ---- (iv)
putting (iv) in (i) we get
\(5100*x/100 = 510\)
or \(x=10\) ---- (v)

putting x=10 in (ii), we get
\(q*(110/100) = 8500\)
or \(q= 8500*(10/11)\) --- (vi)

\(\frac{p}{q}\) = \(\frac{5100}{(8500*(10/11))}\) = \(\frac{5100*11}{8500*10}\) = \(\frac{51*11}{85*10}\) = \(\frac{3*11}{5*10}\) = \(\frac{33}{50}\) = A
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Re: Two persons P and Q lent certain amounts at the same rate of interest   [#permalink] 30 May 2020, 19:41

Two persons P and Q lent certain amounts at the same rate of interest

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