Q. 84.8( 5 Votes )

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

Answer :

Let the units digit be ‘Y’, so the tens digit will be X.


the number is 10X + Y


X . Y =14 –––––– (i)



On simplifying further,


9X – 9Y + 45 = 0


X – Y + 5 = 0


Putting the value of from equation –––––– (i)



14 – Y2 + 5Y = 0


Y2 – 5Y – 14 = 0


On applying Sreedhracharya formula







Y = – 2 or 7


Y = 7 (Only Positive values)



X = 2


The number is 27 {2 (10) + 7}.


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