Ravi invested a total amount of Rs. 65,000 in | vedclass

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(C) Let the amounts invested in schemes $A, B,$ and $C$ be $x, y,$ and $z$ respectively.Given: $x + y + z = 65,000$ $(i)$Given: $x = 0.72z = \frac{18}

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$22$

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(C) Let the amounts invested in schemes $A, B,$ and $C$ be $x, y,$ and $z$ respectively.Given: $x + y + z = 65,000$ $(i)$Given: $x = 0.72z = \frac{18}{25}z$ (ii)Total interest earned in one year: $0.12x + 0.16y + 0.18z = 10,180$Multiply by $100$: $12x + 16y + 18z = 1,018,000$Divide by $2$: $6x + 8y + 9z = 509,000$ (iii)Substitute $x = \frac{18}{25}z$ into $(i)$: $\frac{18}{25}z + y + z = 65,000 \Rightarrow \frac{43}{25}z + y = 65,000 \Rightarrow y = 65,000 - \frac{43}{25}z$ (iv)Substitute $x$ and $y$ into (iii): $6(\frac{18}{25}z) + 8(65,000 - \frac{43}{25}z) + 9z = 509,000$$\frac{108}{25}z + 520,000 - \frac{344}{25}z + 9z = 509,000$$9z - \frac{236}{25}z = 509,000 - 520,000$$\frac{225z - 236z}{25} = -11,000$$-\frac{11}{25}z = -11,000 \Rightarrow z = 25,000$Now,find $y$ using (iv): $y = 65,000 - \frac{43}{25}(25,000) = 65,000 - 43,000 = 22,000$.Thus,the amount invested in scheme $B$ is $Rs. 22,000$.

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