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Ravixxx
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A certain two-digit number has the property that when its are reversed 27 Apr 2020, 10:05
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87% (01:27) correct 13% (03:00) wrong based on 89 sessions

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A certain two-digit number has the property that when its digits are reversed, the resulting number is \(\frac{3}{8}\) of the original number. What is the original number?

(A) 53
(B) 61
(C) 72
(D) 80
(E) 92
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C
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A certain two-digit number has the property that when its are reversed 27 Apr 2020, 13:23
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Ravixxx
A certain two-digit number has the property that when its digits are reversed, the resulting number is \(\frac{3}{8}\) of the original number. What is the original number?

(A) 53
(B) 61
(C) 72
(D) 80
(E) 92
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Let the original two digit number be \(10x+y \)

Upon reversing we get \(10y+x \)= \(\frac{3}{8}(10x+y) \)

simplifying =>\( 80y+8x =30x+ 3y\)\(\hspace{2mm}\)or \(77y=22x \) or\(\hspace{1mm}\) \(7y=2x\) or\(\hspace{2mm}\)\( x=3.5y \)

Putting the value of \(x\) in original number we get \(10(3.5y)+y \) = \(36y\)

Only multiple of 36 among the options is 72

Ans- C
Alternatively one could also pick an option , reverse the digits and check whether the reversed number is \(\frac{3}{8}\) of original number. i.e. \( 27=\frac{3}{8}(72)\)

Hope it's clear .
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A certain two-digit number has the property that when its are reversed 27 Apr 2020, 13:43
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Ravixxx
A certain two-digit number has the property that when its digits are reversed, the resulting number is \(\frac{3}{8}\) of the original number. What is the original number?

(A) 53
(B) 61
(C) 72
(D) 80
(E) 92
Show more

The ratio of the original number to the newly formed number = 8:3
When a two digit number is reversed it increases or decreases by a multiple of 9 ( Notice that, XY -> 10X + Y and YX ->10Y + X and difference 9(X - Y)
Hence the difference here needs to be a multiple of 9.
So 8 : 3 should be changed to 8*9 : 3*9 = 72:27

These are the numbers.
Options C. 72
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A certain two-digit number has the property that when its are reversed 01 Mar 2021, 02:28
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Ravixxx
A certain two-digit number has the property that when its digits are reversed, the resulting number is \(\frac{3}{8}\) of the original number. What is the original number?

(A) 53
(B) 61
(C) 72
(D) 80
(E) 92
Show more


Let the original number be ab which can be written as 10a + b. So the new number will be ba which can be written as 10b + a. Now we are told that 10b + a = 3/8 (10a + b). Upon simplification we get 2a = 7b OR a = 7b/2 Now "a" and "b" have to be "digits and hence b must be divisible by 2. If b = 2 then a = 7 and we get 72 (C)
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A certain two-digit number has the property that when its are reversed 01 Mar 2021, 11:36
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Let's solve it through option: All options are original numbers.

As per the question, the resulting number after reversing the digit is \(\frac{3}{8}\) times the original number. That means the original number should be 8/3 times of reverse number.

So, pick the option that is divisible by '3'- only C = 72

Original number 72.
Reverse = 27

=> \(\frac{3}{ 8}\) * 72(Original) = 27(Resulting).

Answer C
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