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The ratio of a two-digit natural number to a number formed by reversin

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The ratio of a two-digit natural number to a number formed by reversin  [#permalink]

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New post Updated on: 04 Sep 2018, 02:15
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The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

a. 99
b. 198
c. 330
d. 132
e. 282

Originally posted by pratik2018 on 04 Sep 2018, 01:20.
Last edited by pratik2018 on 04 Sep 2018, 02:15, edited 1 time in total.
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Re: The ratio of a two-digit natural number to a number formed by reversin  [#permalink]

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New post 04 Sep 2018, 02:06
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pratik2018 wrote:
The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

a. 99
b. 198
c. 330
d. 132
e. 282


The number should be a multiple of 4 and it's reverse, multiple of 7..
So multiple of 7 with even tens digit..
1) 21 so actual number 12.. ratio 12:21=4:7...yes
Now the next number will be twice 24:42
and next thrice 36:63
and next four times 48:84
The sum = (12+21)*(1+2+3+4)=33*10=330
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Re: The ratio of a two-digit natural number to a number formed by reversin  [#permalink]

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New post 04 Sep 2018, 02:14
let's say that AB/BA =4/7

A and B are both digits

(AB)/(BA) = 4/7=8/14=12/21= 16/28=20/35=24/42=28/49=.....=48/84

For the following multiples of 3 this relationship can be verified

12/24; 21/42; 36/63; 48/84
12+24+21+42+36+63+48+84=330 (Answer C)
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The ratio of a two-digit natural number to a number formed by reversin  [#permalink]

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New post Updated on: 07 Sep 2018, 12:54
The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

a. 99
b. 198
c. 330
d. 132
e. 282

let xy and yx be reversed numbers
difference between reversed numbers will always be a multiple of 9
9/9*4/7=36/63
note 3=6/2
if x=y/2, then 12/21, 24/42, 36/63, and 48/84 are only such two-digit pairs
sum of all such pairs=330
C

Originally posted by gracie on 04 Sep 2018, 08:37.
Last edited by gracie on 07 Sep 2018, 12:54, edited 1 time in total.
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The ratio of a two-digit natural number to a number formed by reversin  [#permalink]

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New post 04 Sep 2018, 08:58
OA: C
Let the number be \(XY\) , where \(X\)= Digit at tens place and \(Y\) = Digit at unit's place
Number formed by reversing the digits \(= YX\)
As per Question

\(\frac{XY}{YX}=\frac{4}{7}\)

\(\frac{10X+Y}{10Y+X}=\frac{4}{7}\)

\(70X+7Y = 40Y+4X\)

\(66X=33Y; \quad 2X=Y\)

Taking \(X=1,\quad Y\) would be \(2\)
Taking \(X=2,\quad Y\) would be \(4\)
Taking \(X=3,\quad Y\) would be \(6\)
Taking \(X=4, \quad Y\) would be \(8\)
Taking X=5,Y would be 10( Not possible as Y is single digit)
Possible value of \(XY : 12,24,36,48\)
Possible value of \(YX : 21,42,63,84\)

Their Sum\(= (12+24+36+48) + (21+42+63+84) = 12(1+2+3+4)+21(1+2+3+4)= 12*10+21*10 =10(12+21)=10*33=330\)
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The ratio of a two-digit natural number to a number formed by reversin   [#permalink] 04 Sep 2018, 08:58
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