Q8 of 168 Page 7

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.

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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