In the sum of four 2-digit numbers, we got 27 more than the true result. This was due to the mistake

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14 Feb 2012 sum

In the sum of four 2-digit numbers, we got 27 more than the true result. This was due to the mistake of reversing the 2 digits of a number out of these four numbers. How many possibilities are there for the number which was printed wrongly

OPtion

1) 9
2) 7
3) 5
4) 8
5) 6
6) 2
7) 3
8) 1
9) 4
10) none of these

Solution

possibilities are 14, 25, 36, 47, 58, 69

Correct Option: 5 Best Solution (7)

Tijo Jose   12 years AGO

Let the number being reversed be 10x + y. (Here, x and y are the digits.)
The reversed number will be 10y + x.
Obviously, 10y + x = 27 + 10x + y
9y = 9x + 27
y = x + 3
All possibilities of (x, y) pairs, and corresponding 2-digit number satisfying these conditions are
(1, 4) = 14
(2, 5) = 25
(3, 6) = 36
(4, 7) = 47
(5, 8) = 58
(6, 9) = 69
So, total 6 possibilities...
(0, 3) is not a choice, as 03 = 3 is not a 2-digit number.

Like? Yes (8) | No (3)  

Dr.Dipin Singh   12 years AGO

such numbers are
14
25
36
47
58
69

so 6 numbers are possible.

Like? Yes (6) | No (3)  

Datla Kanthi   12 years AGO

Correct number can be 14,25,36,47,58 and 69

Like? Yes (3) | No (3)  

shyoram Gurjar   12 years AGO

14 and 41
25 and 52
36 and 63
47 and 74
58 and 85
69 and 96

Like? Yes (4) | No (4)  

Mithlesh Prasad   12 years AGO

41-14=27
52-25=27
63-36=27
74-47=27
85-58=27
96-69=27
so, 6 possible values are there

Like? Yes (2) | No (3)  

Shiv Kumar   12 years AGO

For only 14, 25, 36, 47, 58 and 69 are the only two digit numbers, when we reverse the difference between orginal number and reverse number will be more than 27.

Like? Yes (2) | No (3)  

Sreenivasa Chowdary Nellore   12 years AGO

14, 25, 36, 47, 58 and 69 are the possibilities

Reason is if we assume the two digit number as 'ab' it is represented as '10a+b'

If it is reversed it is 'ba' and represented as '10b+a'

So the difference is [10b+a]-[10a+b] = 27

i.e. 9[b-a] = 27

i.e. b-a = 3,

So the difference between the Units and ten's digit is 3, hence go for trial and error

a b
- -
1 4 rev 41
2 5 rev 52
3 6 rev 63
4 7 rev 74
5 8 rev 85
6 9 rev 96

we can not take '0' for 'a'

Hence there are 6 possibilities only

Like? Yes (1) | No (4)