The annual incomes and expenditures of a man | vedclass

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(A) Let the incomes of the man and his wife be $5x$ and $3x$ respectively.Let the expenditures of the man and his wife be $3y$ and $1y$ respectively.G

Vedclass · Accepted Answer

₹ $5000$,₹ $3000$

Vedclass · Answer

(A) Let the incomes of the man and his wife be $5x$ and $3x$ respectively.Let the expenditures of the man and his wife be $3y$ and $1y$ respectively.Given that they save equally,let the savings of each be $S$. Since the total balance is ₹ $4000$,each saves $S = 4000 / 2 = ₹ 2000$.For the man: $5x - 3y = 2000$ (Equation $1$)For the wife: $3x - y = 2000$ (Equation $2$)From Equation $2$,$y = 3x - 2000$.Substitute $y$ into Equation $1$: $5x - 3(3x - 2000) = 2000$.$5x - 9x + 6000 = 2000$.$-4x = -4000$,so $x = 1000$.Income of the man = $5x = 5 	imes 1000 = ₹ 5000$.Income of the wife = $3x = 3 	imes 1000 = ₹ 3000$.

The annual incomes and expenditures of a man and his wife are in the ratios of $5: 3$ and $3: 1$,respectively. If they decide to save equally and find a balance of ₹ $4000$ at the end of the year (total savings),their incomes were:

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