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The ratio of a two digit number to a number formed by reversing its di 17 Jun 2019, 00:15
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C
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63% (02:44) correct 37% (02:47) wrong based on 265 sessions

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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
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C
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chetan2u
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DisciplinedPrep
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
Show more


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
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DisciplinedPrep
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
Show more

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
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The ratio of a two digit number to a number formed by reversing its di 11 Mar 2024, 07:18
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chetan2u

DisciplinedPrep
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

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
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­chetan2u Why do we consider 21,42,63 and 84? The ratio of those numbers and their reversed digits is 7:4 and not 4:7
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The ratio of a two digit number to a number formed by reversing its di 11 Mar 2024, 07:50
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DisciplinedPrep
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
Show more
\(\frac{­10a + b}{10b + a} = \frac{4}{7}\)­

Or, \(70a + 7b = 40b + 4a\)

Or, \(66a = 33b\)

Or, \(2a = b\)

Now plug in possible values of a and b for a 2 digit no -
Attachment:
Screenshot 2024-03-11 200935.png
Screenshot 2024-03-11 200935.png [ 2.04 KiB | Viewed 2768 times ]
neglect a = 10 and b =5 as 2 digit no can not be formed when a  = 10

Now, find 10a  + b
Attachment:
10a + b.png
10a + b.png [ 1.68 KiB | Viewed 2726 times ]

Again form 10b + a 
Attachment:
10b + a.png
10b + a.png [ 1.58 KiB | Viewed 2711 times ]

Now add (10a + b) + (10b + a) : 
Attachment:
10a + b + 10b +a.png
10a + b + 10b +a.png [ 4.1 KiB | Viewed 2700 times ]
 

Here all the values : \(33 + 66 + 99 + 132 = 330\), Answer must be (C)



 ­
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The ratio of a two digit number to a number formed by reversing its di 25 Mar 2024, 21:24
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chetan2u

DisciplinedPrep
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

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
­chetan2u Why do we consider 21,42,63 and 84? The ratio of those numbers and their reversed digits is 7:4 and not 4:7
Show more

Hi

The numbers are 12, 24, 36 and 48 itself in the solution. However you have to add the pairs that is 12 and 21 plus 36 and 63 and so on.

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The ratio of a two digit number to a number formed by reversing its di 09 Nov 2025, 19:08
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Two digit number, so let xy/yx=4/7

so, 4 is multiplier of xy and 7 is multiplier of yx
given that its two digit number, let multiply 4/7 with same number in numerator and denominator

Case 1 : (4/7)*(2/2)=8/14, but numerator is one digit only so its NA
Case 2: (4/7)*(3/3)=12/21, its two git and reverse to each other so its 1st pair and sum is 33
Case 3 : (4/7)*(6/6)=24/42, its two git and reverse to each other so its 1st pair and sum is 66
Case 4 : (4/7)*(9/9)=36/63, its two git and reverse to each other so its 1st pair and sum is 99
Case 4: (4/7)*(12/12) =48/84, its two git and reverse to each other so its 1st pair and sum is 132
Case 5: (4/7)*(14/14) =56/98, its two digit but not reverse to each other so we can not consider it
Case 6 : (4/7)*(15/15)=60/105, its three digit in denominator so it will not meet the given criteria

So, adding 33+66+99+132=330
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