M4maths Previous Puzzles

01 May 2015 Five digit number

A five digit number has all non-zero different digits & decreasing arranged. Average of all the digits of the numbers is 5. The difference of number and the number formed by reversing the order of digits is 84942. Sum of all such possible digits are

OPtion

1) 196052
2) 196002
3) 195984
4) 195842
5) 195802
6) 195798
7) 195602
8) 195588
9) 195512
10)195490

Solution

Let number is 10000x+1000y+100z+10a+b
Where x not= y not= z not= a not= b not= 0
On reversing digits, we get the new number
10000b + 1000a + 100z + 10y + x
Difference
9999x + 990y - 990a - 999b
= 9999(x-b) + 990(y-a) = 84942
only possible case x-b = 8
so y-a = 5
if x-b = 8
x = 9, b = 1 (Only possibility)
and y-a = 5
(y,a)
(8,3) and (7,2)
So two possible case
x=9 y=8 z=? a=3 b=1 ---------(1)
and x=9 y=7 z=? a=2 b=1 -----(2)
Since average of digit = 45
so z=4 in (1) and z=6 in (2)
So number are
98431
97621
Sum = 196052

Option 1)

Correct Option: 1 Best Solution (17)

Supriya Mondal   9 years AGO

Two numbers are possible. They are 98431 and 97621
So, sum of this two number is=98431+97621=196052
So, option 1)196052 is the right answer

Like? Yes (14) | No (4)  

siva naga kumar   9 years AGO

Let the no. be abcde where a>b>c>d>e
Given = a b c d e = 25
and a b c d e
-e d c b a

8 4 9 4 2
Solve it using cryptographic techniques
1st digit a-e=8,, so take a=9 and e=1
using this d-1 10-b=4 { second last digit }
d 5=b
now take d=2 , b=7 or d=3 , b=8
putting all the values and c a random we get
a= 9 a=9
b= 7 b=8
c= c=
d= 2 d=3
e=1 e=1
Now using given condition a b c d e=25;;
c=6 c=4
Hence nos are 97621 and 98431 and no other case satisfies the conditions in the question ,
97621 98431is equal to
196052

Like? Yes (3) | No   

Madhumoy Gope   9 years AGO

Suppose the no is abcde,such that a>b>c>d>e>0
Now, (a+b+c+d+e)/5=5
Or, a+b+c+d+e=25
By the given condition of (abcde-edcba=84942) if we derive we will get-
9999(a-e) +990(b-d)=84942
Or,1111(a-e)+110(b-d)=9438
From this we will get,a=9,b=(8,7),c=(4,6),d=(3,2),e=1
So,
The possible nos are 98431 & 97621
So,the sum of these 2 nos is 196052

Like? Yes (3) | No   

Aditi Tenguria   9 years AGO

Let the no. be abcde where a>b>c>d>e
Given = a+b+c+d+e = 25
and a b c d e
-e d c b a
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
8 4 9 4 2
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Solve it using cryptographic techniques
1st digit a-e=8,, so take a=9 and e=1
using this d-1+10-b=4 { second last digit }
d+5=b
now take d=2 , b=7 or d=3 , b=8
putting all the values and c a random we get
a= 9 a=9
b= 7 b=8
c= c=
d= 2 d=3
e=1 e=1
Now using given condition a+b+c+d+e=25;;
c=6 c=4
Hence nos are 97621 and 98431 and no other case satisfies the conditions in the question ,
Hence sum = 97621
+98431
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
196052

Like? Yes (3) | No   

Bholanath    9 years AGO

Given points :
1. Average of 5 digits nos. = 5 means sum of digits should be 25
2. Number should be in decreasing order, non- zero and different
3. Difference of Number and reverse of Number = 84942

Overall conclusion:
1. Number must be start with 9 so, the number will be 98521, 98431, 97621, 97531, 96541, 96532
(whose sum is 25)
2. Only the numbers 98431-13489 = 84942, and 97621-12679 = 84942

so, the sum of numbers = 98431+97621= 196052 Ans.

Like? Yes (3) | No (1)  

ankit kamboj   9 years AGO

Let the no. be abcde where a>b>c>d>e
Given = a+b+c+d+e = 25
and a b c d e
-e d c b a
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
8 4 9 4 2
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Solve it using cryptographic techniques
1st digi

Like? Yes (3) | No (1)  

kranthi kanchanapally   9 years AGO

The possible numbers are 97621 and 98431
97621-12679=84942
98431-13489=84942
then the sum of the possible numbers is=97621+98431=196052

Like? Yes (1) | No   

vamsy   9 years AGO

97621-12679=84942
&
98431-13489=84942
Then 97621+98431=196052

Like? Yes (1) | No   

sourav pal   9 years AGO

Let the no. be abcde where a>b>c>d>e
Given = a+b+c+d+e = 25
and a b c d e
-e d c b a
-----------------------
8 4 9 4 2
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Solve it using cryptographic techniques
1st digit a-e=8,, so take a=9 and e=1
using this d-1+10-b=4 { second last digit }
d+5=b
now take d=2 , b=7 or d=3 , b=8
putting all the values and c a random we get
a= 9 a=9
b= 7 b=8
c= c=
d= 2 d=3
e=1 e=1
Now using given condition a+b+c+d+e=25.
c=6 c=4
Hence nos are 97621 and 98431 and no other case satisfies the conditions in the question ,
Hence sum = 97621
+98431
------------------------------
196052

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

numbers are=98431 and 97621
difference between number and reverse is 98431-13489=84942
similarly by 2nd number=97621-12679=84942
sum of both the number is=98431+97621=196052

Like? Yes (2) | No (2)  

umesh   9 years AGO

two such possible no..
are 98431,97621 if we go through the question
sum will be 196052

Like? Yes (1) | No (1)  

~Sandeep~   9 years AGO

98431 13489 84942
97621 12679 84942

Sum of 98431 +97621 = 196052

Like? Yes (1) | No (1)  

SAGNIK DATTA   9 years AGO

Two possible numbers are : 98431 and 97621 which on reversing and subtracting gives 84982 so sum is 196052

Like? Yes (1) | No (1)  

Surya Rajitha   9 years AGO

average of the digits in the number 98431 is (9+8+4+3+1)/5=5

98431-13489=84942

now another possibility is 97621

and their average is also 5 and 97621-12679=84942

sum= 98431+97621=196052

that is option 1

Like? Yes (1) | No (2)  

praveen kumar   9 years AGO

ans 1 is coorect
98432 and 97621 are two possible no

Like? Yes (1) | No (2)  

Surit Datta   9 years AGO

two possible numbers are
97621 and 98431

Like? Yes (1) | No (2)  

neha gupta   9 years AGO

such possible numbers can be only two .They are 97621 and 98431.
Explanation:
as the difference between the number and reverse number is 84942. Therefore first and last digits can be 9 and 1.
Second and fourth digit must have a difference of 5 to obtain the required difference this can be achieved by only two combinations 2 and 7, 3 and 8. therefore numbers are
97621+98431=196052

Like? Yes (1) | No (2)