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The ratio of a two digit number to a number formed by reversing its di
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17 Jun 2019, 00:15
17 Jun 2019, 00:15
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Difficulty:
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Question Stats:
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The ratio of a two digit 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. 110
B. 200
C. 330
D. 88
E. 770
A. 110
B. 200
C. 330
D. 88
E. 770
Re: The ratio of a two digit number to a number formed by reversing its di
[#permalink]
17 Jun 2019, 05:02
17 Jun 2019, 05:02
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Expert Reply
DisciplinedPrep wrote:
The ratio of a two digit 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. 110
B. 200
C. 330
D. 88
E. 770
A. 110
B. 200
C. 330
D. 88
E. 770
Number = 10a+b and its reverse = 10b+a..
So, 10a+b:10b+a=4:7......7(10a+b)=4(10b+a).....70a+7b=40b+4a.....66a=33b....b=2a...
So, numbers are (a)(2a).......12, 24, 36, 48...
Sum = 12+24+36+48+21+42+63+84=330
C
General Discussion
Re: The ratio of a two digit number to a number formed by reversing its di
[#permalink]
17 Jun 2019, 21:08
17 Jun 2019, 21:08
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Kudos
DisciplinedPrep wrote:
The ratio of a two digit 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. 110
B. 200
C. 330
D. 88
E. 770
A. 110
B. 200
C. 330
D. 88
E. 770
let xy and yx be reversed numbers
(10x+y)/(10y+x)=4/7→
2x=y
so xy can have four values: 12, 24, 36, 48
and yx can have four values: 21, 42, 63, 84
sum of eight values=330
C
