An algebra problem by Maneesh .B.Murali

Algebra Level 1

The product of the digits of a two digit number is 14. When 45 is added to the number the place values of its digits get reversed. What is the original two digit number?


The answer is 27.

Maneesh .B.Murali by Maneesh .B.Murali , 22

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4 solutions

Danton Libunao
Mar 7, 2014

let y - tens digit number let x - unit digit number

x*y=14 - first equation y = 14/x

10y + x + 45 = 10x + y - second equation 10x -x - 10y + y = 45 9x - 9y = 45 divide equation by 9 x - y = 5 subtitute value of y x - 14/x = 5 multiply equation by x x^2 -5x - 14 = 0 (x-7)(x+2) = 0 so,, x = 7 y = 14/7 = 2 so the number is 27

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Great! I manually solved it by choosing between 72 and 27..haha

John Shadrach Abalos - 7 years, 3 months ago
Sidra Tariq
Mar 7, 2014

Here it is given that product of two digit is 14, nd 2 and 7 are only its factor..... so the number should be 27 or 72. it is also stated by adding 45 in it the digits xchang their places. So, 27+45=72 nd 72+45=117 hence 27 is the answer

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Salman Asif
Mar 7, 2014

2*7=14 27+45=72

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Anubhav Sharma
Mar 7, 2014

Here, It says that the product of two numbers it 14.

7 and 2 are only the factors of 14.

So, the numbers that can be formed is 27 and 72.

And also add 45 to the small number 27 to get 72. 45 + xy = yx
( xy represents first and second digit NOT the product of x and y )

45 + 27 = 72

Hence, answer is 27

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