Divide ₹ 2379 into 3 parts so that their amou | vedclass

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(D) Let the three parts be $x, y$ and $z$ such that $x + y + z = 2379$.The amount $A$ at simple interest is given by $A = P(1 + \frac{RT}{100})$.Given

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$828$

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(D) Let the three parts be $x, y$ and $z$ such that $x + y + z = 2379$.The amount $A$ at simple interest is given by $A = P(1 + \frac{RT}{100})$.Given that the amounts are equal after $2, 3$ and $4$ years respectively at $5 \%$ rate:$x(1 + \frac{5 	imes 2}{100}) = y(1 + \frac{5 	imes 3}{100}) = z(1 + \frac{5 	imes 4}{100}) = k$$x(1 + \frac{1}{10}) = y(1 + \frac{3}{20}) = z(1 + \frac{1}{5}) = k$$\frac{11x}{10} = \frac{23y}{20} = \frac{6z}{5} = k$Thus,$x = \frac{10k}{11}, y = \frac{20k}{23}, z = \frac{5k}{6}$.Substituting these into $x + y + z = 2379$:$\frac{10k}{11} + \frac{20k}{23} + \frac{5k}{6} = 2379$Taking the $LCM$ of $11, 23, 6$,which is $1518$:$\frac{1380k + 1320k + 1265k}{1518} = 2379$$\frac{3965k}{1518} = 2379$$k = \frac{2379 	imes 1518}{3965} = 910.8$Now,$x = \frac{10 	imes 910.8}{11} = 828$.Therefore,the first part is ₹ $828$.

Divide ₹ $2379$ into $3$ parts so that their amounts after $2, 3$ and $4$ years respectively may be equal,the rate of interest being $5 \%$ per annum at simple interest. The first part is (in ₹):

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