Q35 of 40 Page 1

A two-digit number is such that the product of its digit is 14. If 45 is added to the number; the digits interchange their places. Find the number.

Let the digit on units place be x & on that place be y.

∴ The original number = 10y + x and number with interchanged digits = 10x + y


A.T.Q


x.y=14..(i)


(10y+x)+45=10x+y


→ 9x-9y=45


Or x-y=5


X=5+y…(ii)


Substitute the value of x in (i)


Y(5+y)=14


5y+y2=14


Y2+5y-14=0


Y2+7y-2y-14=0


Y(y+7)-2(y+7)=0


(y+7)(y-2)=0


Y=-7 and y=2


Neglecting y = -7


Now, put y = 2 in eq…(i)


X(2) =14


X=7


∴ The number = 10y+x=10(2)+7=27


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