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SSC Sample Paper SSC-CGL TIER - I Sample Test Paper-10

  • question_answer
    A two digit number contains the smaller of the two digits in the unit's place. The product of the digits is 24 and the difference between the digits is 5, then the digit at ten's place is:

    A) 6                                 

    B) 8

    C) 4                                 

    D) None of the above

    Correct Answer: B

    Solution :

    Let the digit at unit's place be x and the digit at ten's place = y such that x < y. Two digit number = 10y + x Product of the digit = xy = 24 Difference between digits =   \[y-x=5\]                                         ... (i) \[\therefore \,\,\,\,\,x<y\therefore {{\left( x+y \right)}^{2}}={{\left( x-y \right)}^{2}}+4xy\] \[=\,\,\,\,\,\,{{5}^{2}}+4\times 24=121\] \[\Rightarrow \,\,\,\,\,\,x+y=11\]                           ... (ii) Adding (i) & (ii), we have \[2y=16\Rightarrow y=8\] Shortcut method:- Product of digits \[=24=8\times 3\] Difference between digits = 5 Which satisfies the question Hence, digit at ten's place = [8]


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