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The sum of the digits of a two digit number is 10. When the digits are

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vomhorizon
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The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   14 Nov 2012, 08:34
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The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.

(A) 28
(B) 19
(C) 37
(D) 46


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Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y

According to the Question Stem: X + Y = 10

When the number is reversed we get 10Y+X as the new number.

According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.

Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)

Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A)
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   14 Nov 2012, 10:14
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a+b = 10
10a + b - 10b - a = 54
a-b = 6

a= 8, b = 2.

Reversed number is 28.

Kudos Please... If my post helped.
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   14 Nov 2012, 08:43
vomhorizon wrote:
The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.

(A) 28
(B) 19
(C) 37
(D) 46


Show Spoiler
Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y

According to the Question Stem: X + Y = 10

When the number is reversed we get 10Y+X as the new number.

According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.

Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)

Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A)


Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6
Only option A satsifies this.

Ans A it is.
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   14 Nov 2012, 19:29
Vips0000 wrote:
vomhorizon wrote:
The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.

(A) 28
(B) 19
(C) 37
(D) 46


Show Spoiler
Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y

According to the Question Stem: X + Y = 10

When the number is reversed we get 10Y+X as the new number.

According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.

Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)

Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A)


Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6
Only option A satsifies this.

Ans A it is.



Can you further explain this in detail? How did you get 54/9 ? Where did the 9 come from?
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   14 Nov 2012, 20:47
watwazdaquestion wrote:
Vips0000 wrote:
vomhorizon wrote:
The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.

(A) 28
(B) 19
(C) 37
(D) 46


Show Spoiler
Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y

According to the Question Stem: X + Y = 10

When the number is reversed we get 10Y+X as the new number.

According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.

Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)

Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A)


Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6
Only option A satsifies this.

Ans A it is.



Can you further explain this in detail? How did you get 54/9 ? Where did the 9 come from?

This 9 is logical derivation. Difference between a 2 digit number and number with reversed digit is always 9 times the difference between digits.
Any number 10a+b when reversed would be 10b+a , the difference would be 9(b-a)
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink] New post   24 Jan 2024, 07:36
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vomhorizon wrote:
The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.

(A) 28
(B) 19
(C) 37
(D) 46

Check using options -

Here \(a + b\) in all cases in \(10\)

\((A) 82 - 28 = 54\)
\((B) 91 - 19 = 72\)
\((C) 73 - 37 = 36\)
\((D) 64 - 46 = 18\)

AMong the given options only (A) fits in perfectly, hence Answer must be (A)
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Re: The sum of the digits of a two digit number is 10. When the digits are [#permalink]
24 Jan 2024, 07:36
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