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SSC Quantitative Aptitude Ratio and Proportion Question Bank Ratio and Proportion (II)

  • question_answer
    A and B have their monthly incomes in the ratio 8 : 5, while their monthly expenditures are in the ratio 5 : 3. If they have saved Rs. 12000 and Rs. 10000 monthly respectively, then the difference in their monthly income is [SSC CGL Tier II, 2015]

    A) Rs. 46000

    B) Rs. 42000

    C) Rs. 44000

    D) Rs. 52000

    Correct Answer: B

    Solution :

    [b] Let, the monthly income of A and B be Rs. 8x and Rs. 5x and monthly expenditure Rs. 5y and Rs. 3y respectively. Then, According to the questions, \[\frac{8x-5y}{5x-3y}=\frac{12000}{10000}\] \[\Rightarrow \]\[(8x-5y)\times 5=(5x-3y)\times 6\]                           \[\Rightarrow \]\[40x-25y=30x-18y\] \[\Rightarrow \]   \[10x=7y\] \[\therefore \]      \[50x=35y\]                               …(i) \[\therefore \]      \[8x-5y=12000\] \[\Rightarrow \]   \[56x-35y=84000\] \[\Rightarrow \]   \[56x-50x=84000\]         [from Eq. (i)] \[\Rightarrow \]   \[6x=84000\] \[\therefore \]      \[x=14000\] Required difference \[=8x-5x=3\times 14000=\text{Rs}.\,\,42000\]


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