10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Pair of Linear Equations in Two Variables

  • question_answer The sum of two numbers is 8 and the sum 8 of their reciprocals is\[\frac{8}{15}\]. Find the numbers.

    A)  5, 3                            

    B)  7, 1    

    C)         4, 4    

    D)                     2, 6 

    Correct Answer: A

    Solution :

    Let the two numbers be x and y. According to the given conditions, \[x+y=8~\]                                        ....(1) and   \[\frac{1}{x}+\frac{1}{y}=\frac{8}{15}\]                              ....(2) Putting value of \[x=8-y\]in (2), we get \[\frac{1}{8-y}+\frac{1}{y}=\frac{8}{15}\]   \[\Rightarrow \]  \[\frac{y+8-y}{y(8-y)}=\frac{8}{15}\] \[\Rightarrow \]\[{{y}^{2}}-8y+15=0\]\[\Rightarrow \] \[{{y}^{2}}-5y-3y+15=0\] \[\Rightarrow \]\[(y-5)\,(y-3)=0\] \[\Rightarrow \]\[y=5\] or \[y=3\] From (1), \[x=3\]or \[x=5\] Thus, the numbers are 5 and 3.

adversite


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