Question

Find the as
The sum of the digits of a two-digit number is 14, The number is nineteen times the
digit at its ones place. Find the number.


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Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Sum of the digits of two digit number is 14}$

$\textsf{The number is nineteen times the digit at its ones place}$

$\underline{\textsf{To find:}}$

$\textsf{Find the number}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the two digit number be 10x+y}$

$\textsf{Sum of the digits=14}$

$\implies\mathsf{x+y=14}$......(1)

$\textsf{Also,}$

$\mathsf{10x+y=19y}$

$\implies\mathsf{10x-18y=0}$

$\implies\mathsf{5x-9y=0}$.....(2)

$\textsf{Solving (1) and (2)}$

$\mathsf{9x+9y=126}$

$\mathsf{5x-9y=0}$

$\implies\mathsf{14x=126}$

$\implies\mathsf{x=\dfrac{126}{14}=9}$

$\mathsf{(1)\implies\,y=5}$

$\therefore\textsf{The required number is 10(9)+5}$

$\mathsf{95}$