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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Two persons P and Q lent certain amounts at the same rate of interest

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Manager  S
Joined: 01 Jun 2019
Posts: 72
Two persons P and Q lent certain amounts at the same rate of interest  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 40% (01:53) correct 60% (03:41) wrong based on 10 sessions

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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
Kellogg School Moderator B
Joined: 25 Aug 2015
Posts: 44
GMAT 1: 590 Q48 V21
GMAT 2: 620 Q49 V25
Re: Two persons P and Q lent certain amounts at the same rate of interest  [#permalink]

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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 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  