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in Quadratic Equations by (55.4k points)
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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.

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Best answer

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

∴ the number is 10X + Y

X . Y =14 –––––– (i)

10X + Y + 45 = 10Y + X

On simplifying further,

9X – 9Y + 45 = 0

X – Y + 5 = 0

Putting the value of x = 14/Y from equation –––––– (i)

14/Y - Y + 5 = 0

14 – Y2 + 5Y = 0

Y2 – 5Y – 14 = 0

On applying Sreedhracharya formula

Y = – 2 or 7

∴ Y = 7 (Only Positive values)

X = 14/7

∴ X = 2

∴ The number is 27 {2 (10) + 7}.

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