Ten\'s digit of a two digits number is greater by 7 than the unit\'s digit. Sum of the digits is 1/9

M4maths Previous Puzzles

06 Jun 2013 Number

Ten's digit of a two digits number is greater by 7 than the unit's digit. Sum of the digits is 1/9 of that number. Find the number.

OPtion

1) 63
2) 97
3) 18
4) 79
5) 81
6) 27
7) 36
8) 48
9) 56
10) None of these

Solution

Let unit's digit be x and Ten's digit be y and Number 10y+x
Now according to the question
y=7+x (i)
x+y=1/9(10y+x) (ii)
Solving (i) and (ii)
we get y=8 and x=1
Number 10y+x = 10*8+1
81
option 5

Correct Option: 5 Best Solution (24)

Pargat Pal Singh   11 years AGO

Ten's digit of a two digits number is greater by 7 than the unit's digit.

Unit digit can be 1 or 2 only .
check 81 and 92.

only 81 satisfies second condition i.e.
Sum of the digits is 1/9 of that number. Find the number.

so 81 is required number.

Like? Yes (12) | No (1)  

Dr.Dipin Singh   11 years AGO

T=U+7
10T +U= 9*(T+U)
T= 8U= U+7
7U=7
U=1
T=8

so number is 81.

Like? Yes (9) | No (1)  

jaspreet kaur   11 years AGO

y-x=7
x+y=1/9(10y+x)
solvin above two
x=1
y=8

Like? Yes (5) | No (1)  

vinod   11 years AGO

let the number be 10x+y
given that x=y+7
also (x+y)=(1/9)(10x+y)
solving gives x=8, y=1
so the number is 81

Like? Yes (3) | No   

Thaiyalnayaki   11 years AGO

1+7=8 which is the ten\'s place number
sum=9
digit=81
therefore 9/81=1/9

Like? Yes (3) | No   

vigneshwari   11 years AGO

Let the two digit number be 10x+y where 10's digit is x and unit's digit is y.
Then we have, x = 7+y => x-y = 7 ....(1)
And, x+y = (1/9)(10x+y)
=> x-8y = 0 ...(2)
Solving (1) and (2), we get x=8 and y=1.
Hence the required number is 10(8)+1 = 81.

Like? Yes (3) | No (1)  

SANJAY BHANDARI   11 years AGO

sum of digit 9 which is 1/9 of no 81 and digits difference is 7..

Like? Yes (1) | No   

Murali Krishna   11 years AGO

81/9= 9
9=8+1

Like? Yes (1) | No   

Balakrishnan M   11 years AGO

Ten's digit of a two digits number is greater by 7 than the unit's digit.
In 81, 8 is greater by 7 then 1.
8+1=9 = 81*(1/9)

Like? Yes (1) | No   

enthura90   11 years AGO

x-y=7;x+y=1/9(10x+y)

Like? Yes (1) | No   

Adarsha Upadhya   11 years AGO

2 digits no.=xy=10x+y------3
from problem x=y+7------1
x+y=1/9XY-----2

substitute 3 in 2 we get x+y=1/9[11y+70]------4
substitute 1 in 4 we get y=1 and x=y+7 that is x=8;
therefore the num is 81

Like? Yes (1) | No   

Anil Kumar Bharti   11 years AGO

Ans: 5) 81
Exp:
Let unit digit=x
ten's digit=7+x
by ques...
7+x+x=1/9{(10*(7+x)+x}
After solve
x=1
then unit digit=1
ten's digit=8
number will be 81

Like? Yes (1) | No   

Anbalagan K   11 years AGO

Answer : 81
8 is greater by 7 than 1
8+1=9 which is 1/9 of the number 81

Like? Yes (1) | No   

sanjay singh   11 years AGO

let x be at ten's digit and y be units digit
x-y=7
and x+y=(10x+y)/9
solving we get
x=8 and y=1
so,the number is 81

Like? Yes (1) | No   

Prateek Sancheti   11 years AGO

Let x be the unit digit and y be the ten's digit and given:
y=x+7 -----(1)
also x+y=1/9(x+10y) ------(2)
Using equation 1 in 2 we get
x=1 and y=8
And two digit number is : (x+10y) = (1+80) =81

Like? Yes (3) | No (2)  

Satyaranjan   11 years AGO

Suppose the no is 10x+y
given x-y=7
and x+y=1/9(10x+y)
Solving these eqs we can get x=8 and y=1

Like? Yes (1) | No   

Browns MN   11 years AGO

81 satisfies above two conditions...

Like? Yes (1) | No   

Jigyasa Kumar   11 years AGO

Answer=81
shortcut : just by looking at the options we can guess the answer.the question says ten\'s digit is greater by 7 than the unit\'s digit .so 81 will be the correct answer since 8-1=7

Like? Yes (2) | No (2)  

Mahesh Nakala   11 years AGO

let ab be no.==10a+b
a=b+7
9(a+b)=10a+b
a-8b=0
so a=8;b=1
Total 10a+b=ab=81

Like? Yes (1) | No (1)  

IFFAT IRAM   11 years AGO

let the two digit no. be 10x+y
x=y+7 ....(1)
x+y=(10x+y)/9
=> x-8y=0 ....(2)
solving (1) & (2)
x=8 & y=1
no. is 81
option 5

Like? Yes (2) | No (3)  

ajitha   11 years AGO

let us take the two digits number as xy means The two digits number xy=10x+y
Condition 1:x=7+y
condition 2:x+y=1/9(10x+y)
by soving the above eq'ns will get x=8 and y=1
Hence the number is 81

Like? Yes (1) | No (2)  

django   11 years AGO

let number be xy.....x-y=7....and x+y=(10x+y)*1/9

Like? Yes (1) | No (2)  

Devendra Marghade   11 years AGO

If the tens & unit digits of the number are x & y
Number=10x+y
Given x=y+7 ---(i) & x+y=(10x+y)/9 or x=8y ---(ii)
Solving (i) & (ii), we have x=8, y=1
So number=81

Like? Yes (1) | No (2)  

Vinay Sipani    11 years AGO

Units digit = x => Ten's digit = (x + 7)

=>The number is 10(x + 7) + x
= 11x + 70

Sum of digits = (2x + 7)

=> (2x + 7) = (11x + 70)/9
=> x = 1 , (x + 7) = 8
=> number is 81

Like? Yes (1) | No (4)