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A number of two digits is such that the sum of the digits is 11, and the number is 27 greater that the number obtained by reversing the digits. Find the number.

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by shaalladin

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by shaalladin

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As sum of digits = 15, then T + U = 15

The value of this number is: 10(T) + U. or 10T + U, and when reversed, we have: 10(U) + T, or 10U + T

Since the # formed by reversing the digits is 27 less than the original number, then we can say that:

10U + T = 10T + U – 27 --------> – 9T + 9U = -27

We now have the following simultaneous equations:

T + U = 15 _____ (i)

– 9T + 9U = - 27 _____ (ii)

9T + 9U = 135 _______ (iii) ----- Multiplying eq (i) by 9

18U = 108 _______ Adding eq (ii) and eq (iii)

U, or the units digit = , or

Substituting 6 for U in eq (i), we get: T + 6 = 15 ----- T, or the tens digit =

Now, since the tens digit is 9, and the units digit is 6, this makes the number:

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Such that, x + y = 11 ....(1)

The number is 10x + y

The digits are

the new number = 10y + x

Original number is 27 more than the new number

10x + y = 10y + x + 27

9x - 9y = 27

x - y = 3 ...(2)

On solving the equations (1) and (2)

x = 7 and y = 4

The number is 74.