A sum of ₹ 7700 is to be divided among three | vedclass

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(A) Let the shares of Vikas,Vijay,and Viraj be $P_1, P_2,$ and $P_3$ respectively.Given that the simple interest on each part is equal at $R = 5 \%$ $

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$2800$

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(A) Let the shares of Vikas,Vijay,and Viraj be $P_1, P_2,$ and $P_3$ respectively.Given that the simple interest on each part is equal at $R = 5 \%$ $p.a.$Simple Interest $SI = \frac{P 	imes R 	imes T}{100}$.For Vikas: $SI_1 = \frac{P_1 	imes 5 	imes 1}{100} = \frac{5P_1}{100}$.For Vijay: $SI_2 = \frac{P_2 	imes 5 	imes 2}{100} = \frac{10P_2}{100}$.For Viraj: $SI_3 = \frac{P_3 	imes 5 	imes 3}{100} = \frac{15P_3}{100}$.Since $SI_1 = SI_2 = SI_3$,we have $5P_1 = 10P_2 = 15P_3$.Dividing by $5$,we get $P_1 = 2P_2 = 3P_3$.To find the ratio $P_1 : P_2 : P_3$,we take the $LCM$ of $1, 2,$ and $3$,which is $6$.$P_1 = 6k, 2P_2 = 6k \implies P_2 = 3k, 3P_3 = 6k \implies P_3 = 2k$.The ratio $P_1 : P_2 : P_3 = 6 : 3 : 2$.Total sum $= 6k + 3k + 2k = 11k = 7700$.$k = \frac{7700}{11} = 700$.Share of Vikas $= 6 	imes 700 = ₹ 4200$.Share of Viraj $= 2 	imes 700 = ₹ 1400$.Difference $= 4200 - 1400 = ₹ 2800$.

$A$ sum of ₹ $7700$ is to be divided among three brothers Vikas,Vijay,and Viraj in such a way that the simple interest on each part at $5 \%$ $p.a.$ after $1, 2,$ and $3$ years,respectively,remains equal. The share (in ₹) of Vikas is more than that of Viraj by:

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