Question

The annual incomes of $A$ and $B$ are in the ratio $3:4$ and their annual expenditures are in the ratio $5:7$. If each saves $5,000$ Rs.; find their annual incomes.

• A. $A=10,000$ Rs. and $B=20,000$ Rs.
• B. $A=30,000$ Rs. and $B=40,000$ Rs.
• C. $A=16,000$ Rs. and $B=24,000$ Rs.
• D. $A=42,000$ Rs. and $B=16,000$ Rs.

Answer 1

Answer: (B)

$A=30,000$ Rs. and $B=40,000$ Rs.

$LetAand{B}^{\prime }sincomesbe3xand4xLettheirexpenditurebe5yand7yresp.SavingsofA=3x-5y=5000->1SavingsofB=4x-7y=5000->2So3x-5y=4x-7yx=2y->3Subx=2yineqn1,wegety=5000x=2y=10000A^{\prime }sannualincome=3x=Rs30,000B^{\prime }sannualincome=4x=Rs40,000$