10th Class Mathematics Solved Paper - Mathematics-2015 Term-I

  • question_answer The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

    Answer:

    Let unit digit \[=x\]
    Tens digit \[=y\]
    So, original number \[=\text{unit digit}+10\times \text{tens digit}\]
                                 \[1=x+10y\]
    According to question,
    Sum of digits \[=8\]
    so,        \[x+y=8\]                                                         ...(i)
    On reversing the digits, unit digit \[=y\], Tens digit \[=x\]
    So,   New number \[=10x+y\]
    According to question,
    Difference \[=18\]
    \[\Rightarrow \,x+10y-(10x+y)=18\]
    \[\Rightarrow \,x+10y-10x-y=18\]
    \[\Rightarrow \,9y-9x=18\]
    \[\Rightarrow \,y-x=2\]                                                    ...(ii)
    By adding eq. (i) and (ii)
               \[2y=10\]
                \[y=\frac{10}{2}\Rightarrow y=5\]
    Put the value of y in eq. (i)
                \[x+y=8\]
    \[\Rightarrow x+5=8\]
    \[\Rightarrow x=8-5\]
    \[\Rightarrow x=3\]
    \[\therefore \] Original number \[=10y+x\]
                                 \[=10\times 5+3\]
                                 \[=50+3\]
                                 \[=53\]


adversite


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