Divide Rs. 4758 into three parts such that th | vedclass

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(B) Let the three parts be $P_1, P_2,$ and $P_3$. The amount $A$ after $t$ years at a simple interest rate $r = 5 \%$ is given by $A = P(1 + \frac{rt}

Vedclass · Accepted Answer

$1656$

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(B) Let the three parts be $P_1, P_2,$ and $P_3$. The amount $A$ after $t$ years at a simple interest rate $r = 5 \%$ is given by $A = P(1 + \frac{rt}{100})$.For $t = 2, 3, 4$ years,the amounts are:$A_1 = P_1(1 + \frac{5 	imes 2}{100}) = P_1(1 + 0.1) = 1.1P_1 = \frac{110}{100}P_1$$A_2 = P_2(1 + \frac{5 	imes 3}{100}) = P_2(1 + 0.15) = 1.15P_2 = \frac{115}{100}P_2$$A_3 = P_3(1 + \frac{5 	imes 4}{100}) = P_3(1 + 0.2) = 1.2P_3 = \frac{120}{100}P_3$Given $A_1 = A_2 = A_3$,we have $110P_1 = 115P_2 = 120P_3$.Dividing by $5$,we get $22P_1 = 23P_2 = 24P_3$.The ratio $P_1 : P_2 : P_3 = \frac{1}{22} : \frac{1}{23} : \frac{1}{24}$.Multiplying by the $LCM$ of $22, 23, 24$ (which is $22 	imes 23 	imes 12 = 6072$):$P_1 : P_2 : P_3 = 276 : 264 : 253$.Sum of ratios $= 276 + 264 + 253 = 793$.$P_1 = \frac{276}{793} 	imes 4758 = 276 	imes 6 = 1656$.Thus,the $1^{	ext{st}}$ part is $Rs. 1656$.

Divide $Rs. 4758$ into three parts such that their amounts after $2, 3,$ and $4$ years respectively are equal,given the rate of interest is $5 \%$ per annum. Find the amount of the $1^{\text{st}}$ part (in $Rs.$).

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