A sum of Rs 7,930 is divided into 3 parts and | vedclass

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(A) Let the parts given to $A, B,$ and $C$ be $P_A, P_B,$ and $P_C$ respectively.Given that the total amount (Principal + Interest) is equal for all t

Vedclass · Accepted Answer

$2760$

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(A) Let the parts given to $A, B,$ and $C$ be $P_A, P_B,$ and $P_C$ respectively.Given that the total amount (Principal + Interest) is equal for all three.Amount = $P(1 + \frac{RT}{100})$.For $A$: $P_A(1 + \frac{5 	imes 2}{100}) = P_A(1.10) = 110\% P_A$.For $B$: $P_B(1 + \frac{5 	imes 3}{100}) = P_B(1.15) = 115\% P_B$.For $C$: $P_C(1 + \frac{5 	imes 4}{100}) = P_C(1.20) = 120\% P_C$.Equating them: $110 P_A = 115 P_B = 120 P_C = K$.$P_A : P_B : P_C = \frac{1}{110} : \frac{1}{115} : \frac{1}{120} = \frac{1}{22} : \frac{1}{23} : \frac{1}{24}$.Multiplying by the $LCM$ $(22 	imes 23 	imes 24 = 12144)$:$P_A : P_B : P_C = (23 	imes 24) : (22 	imes 24) : (22 	imes 23) = 552 : 528 : 506$.Dividing by $2$: $276 : 264 : 253$.Sum of ratios = $276 + 264 + 253 = 793$.$P_A = \frac{276}{793} 	imes 7930 = 2760$.

$A$ sum of $Rs$ $7,930$ is divided into $3$ parts and given on loan at $5 \%$ simple interest to $A, B$ and $C$ for $2, 3$ and $4$ years respectively. If the amounts (principal + interest) of all three are equal after their respective periods of loan,then the amount $A$ received as a loan is:

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