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8th Class Mathematics Linear Equations in One Variable Question Bank Linear Equations in One Variable

  • question_answer
    The sum of two numbers is 10. One of the numbers is equal to the sum of 6 and twice the other number. What is the difference of the numbers?

    A)  \[5\frac{1}{4}\]                               

    B)                         \[8\frac{1}{2}\]

    C)                         \[7\frac{1}{3}\]                               

    D)                         \[6\frac{2}{3}\]

    Correct Answer: C

    Solution :

    Let the numbers be 'x' and y. Then \[x+y=10\]and \[x=6\text{+}2y\]. \[\Rightarrow \]               \[6+2y+y=10\] \[\Rightarrow \]               \[3y=10-6\] \[\Rightarrow \]               \[y=\frac{4}{3}\] \[\therefore \]     \[x=6+2\left( \frac{4}{3} \right)=6+\frac{8}{3}=\frac{26}{3}\] Therefore, the required difference \[=\frac{26}{3}-\frac{4}{3}=\frac{22}{3}=7\frac{1}{3}\]


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