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The difference between a two-digit number and the number obtained by i

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New post Updated on: 09 Apr 2019, 10:43
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The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 2 : 1 ?

a. 4

b. 8

c. 16

d. 20

e. None of these

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Originally posted by AkshdeepS on 08 Apr 2019, 23:05.
Last edited by AkshdeepS on 09 Apr 2019, 10:43, edited 1 time in total.
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Re: The difference between a two-digit number and the number obtained by i  [#permalink]

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New post 09 Apr 2019, 10:24
Let the two digit number be 10x+y
And the number obtained after interchanging be 10y+x
Difference = 9(x-y) = 36
x-y = 4
Possible combinations are (5,1) (6,2) (7,3) (8,4) (9,5)
Also, given that the ratio of the digits is 1:2
Only combination possible is (8,4)
Sum of the digits = 8+4 = 12
Difference of the digits = 8-4 = 4
Difference between these two is 12-4 = 8

B is the answer.

AkshdeepS, I think the ratio should be 2:1. As the difference between the numbers after interchanging is positive.
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Re: The difference between a two-digit number and the number obtained by i  [#permalink]

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New post 09 Apr 2019, 10:34
Explanation

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let ten's and unit's digits be 2x and x respectively.

Then, (10 x 2x + x) - (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) - (2x - x) = 2x = 8.

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Re: The difference between a two-digit number and the number obtained by i  [#permalink]

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New post 09 Apr 2019, 10:42
Chethan92 wrote:
Let the two digit number be 10x+y
And the number obtained after interchanging be 10y+x
Difference = 9(x-y) = 36
x-y = 4
Possible combinations are (5,1) (6,2) (7,3) (8,4) (9,5)
Also, given that the ratio of the digits is 1:2
Only combination possible is (8,4)
Sum of the digits = 8+4 = 12
Difference of the digits = 8-4 = 4
Difference between these two is 12-4 = 8

B is the answer.

AkshdeepS, I think the ratio should be 2:1. As the difference between the numbers after interchanging is positive.


Your point is valid. Ratio comes out to be 2:1. Though question above has the same wordings as written in the official source, I make the necessary change.
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The difference between a two-digit number and the number obtained by i  [#permalink]

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New post 09 Apr 2019, 20:14
AkshdeepS wrote:
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 2 : 1 ?

a. 4

b. 8

c. 16

d. 20

e. None of these


difference between digits=36/9=4
if ratio is 2:1, digits must be 8 and 4
(8+4)-(8-4)=8
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Re: The difference between a two-digit number and the number obtained by i  [#permalink]

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New post 17 Apr 2019, 14:03
It's written that the ratio between the numbers is 2:1.

So the only two-digit numbers that could be are:

x y

2 1
4 2
6 3
8 4

\(84-48 = 36\)

So \(8 + 4 = 12\) and \(8 - 4 = 4\)

\(12 - 4 = 8\)

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Re: The difference between a two-digit number and the number obtained by i   [#permalink] 17 Apr 2019, 14:03
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