# Aptitude - Problems on Numbers - Discussion

Discussion Forum : Problems on Numbers - General Questions (Q.No. 4)
4.
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
4
8
16
None of these
Explanation:

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let ten's and unit's digits be 2x and x respectively.

Then, (10 x 2x + x) - (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) - (2x - x) = 2x = 8.

Discussion:
45 comments Page 1 of 5.

Pooja said:   10 years ago
Hello Friends,

Suppose x & y two digits and the ratio b/w the digits of the number is 1:2

Therefor, x:y = 1:2
So, y = 2x ..........equation 1.

Hence, y is in ten's position and x is in unit place.

According to the question,
(10y + x) - (10x + y) = 36

From equation 1, we get y = 2x
(10*2x + x ) - (10x + 2x) = 36
(20x + x) - (12x) = 36
21x - 12x = 36
9x = 36
x = 4 ........... equation 2.

Now putting the value of x in equation 1.
y = 2*4
y = 8

Sum and the difference of the digits of the number (x + y) & (x - y) respectively.

According to question,
Difference between (x + y) & (x - y).
= (y+ x) - (y - x) ............. equation 3.

Putting the value of x = 4 & y = 8 in the above equation.
We get,
= (8 + 4) - (8 - 4).
= 12 - 4.
= 8.

KHY said:   7 months ago
So after devoting 30 min, finally I got this! Hopes this will help you all.

Let's take a two-digit no. = XY( 10x +y)

Imp =suppose 27=2 @tenth +7 @unit)

Ist condition:
Ratio is 1:2
Let's assume x = a.
Y= 2a.

10x+y = 10 *a +2a = 10a + 2a = 12a --->(1)
10y+x = 10 * 2a +a =20a + a = 21a ---> (2).

Difference between.
21a - 12a = 36,
9a = 36,
a = 4.

So,
Fill the value in (1,(2).
I.e. 12a =12*4 = 48
21a = 21*4 = 84.
Sum of digits=4 +8 = 12.
Difference = 8-4 = 4.
Differ. between sum and subtraction,
12-4 = 8.
Hope, I am able to explain you simply as possible.
(29)

Here we have

The difference between a two-digit number and the number obtained by interchanging the digits is 36
let a,b be 2 numbers
so, a-b=36

ratio between the digits of the number is 1 : 2
let x,y be d digits of a number
x/y=1/2
so, y=2x

now a must be greater than b
here we can see y is greater than x
here
for a => y is ten's digit n x is unit's
for b => x is ten's digit n y is unit's

so (10y+x)-(10x+y)=36
(10*(2x)+x)-(10x + 2x)=36
(21x)-(12x)=36
9x=36
x=4

(y+x)-(y-x)=(x+2x)-(2x-x)=2x=8

Sivasankaran said:   4 years ago
The given number is 36 which is +ve So the original number should be greater
Ex:
If ab is two-digit number b is in unit place and a is in 10th place (.etc..hundreds, tens, units)

Now the given ratio is 1:2 says that the ratio between 10s or 1s
The first number must greater than the reverse digit number.
So we give 2x in 10th place in the first number.
(Number)(10*2x+x)-(Reverse no-Small)(10x+2x)=36.
By solving X=4.

Then they said to find the sum and diff of number.
Ans=(2x+x)-(2x-x).
By solving;
We get the Ans is 8.
(4)

At first we should decide the digits of 10's & unit's be X & 2X respectively.
((10 x 2X) + X) - ((10 x X) + 2X) = 36
(20X + X) - (10X + 2X) = 36
21X - 12X = 36
9X = 36
X = 4
The difference between two digits = (2X+X)-(2X-x)
= 3X - X
= 2X
= 2(4)
= 8
(1)

Once u find x then try this method to get the answer

21X-12X
21(4)-12(4)
84-48

that means the two number are 84 and 48..

now we have to take the sum of one no and the difference of other no.. according to question sum of digits and difference of digits
that is

48=4+8=12(sum of digits)

84=8-4=4(diff of digits)

now the difference of these two answer

12-4=8

Let x and y be two digits of the Numbers.
Such that x is in tens position and y is at the ones place
So xy is the number
xy = 10(x) + y(1) ----------> (1)
On interchanging the digits we get
yx = y(10) + x(1) ----------> (2)
(10x + y) - (10y + x)= 36
10x + y - 10y - x = 36
9x - 9y = 36
x - y = 4
Let,
x = 2a
y = a
Then,
a = 4
Difference =
(8 + 4) - ( 8 - 4)
12 - 4 = 8

AMIT RANJAN said:   6 years ago
Suppose we take two nos as X & Y,
then, 10X+Y-10Y-X=36
=> 9X-9y=36 =>X-Y=4 ---> (A)
Given, X:Y = 1:2 => X = Y/2
Now from eq (A) , Y/2 - Y = 4 => -Y/2 = 4 => Y= -8 ---> (B)
A/Q, (X + Y) - (X - Y) = ?
=> X + Y - X + Y= ? => 2Y = ? ---> (C)

So from (B) putting the value of 'Y' in (C),
2Y = 2 * (-8) = -16 ANS.

Aditrya tiwari said:   8 years ago
Consider no is 10x + y.
Then according to first condition (10x + y) - (10y + x) = 36.
On solving this we get, (x - y) = 4.
In, the last condition they give, y/x = 1/2.
By solving both above equations we get y = 4.

They ask the value for,(10x + y) - (10x - y).
Which is equal to 2y.
Put the value of y.

We get final value = 8.
(3)

Let digit at 10th place X and unit place Y.

From the question:

10X+Y-(10Y+X) = 36.

So, 10X-X+Y-10Y = 36.

= 9X-9Y = 36.

= X-Y = 4.

From question Ratio is 1x:2x.

Difference between the ratio 1x.

So 1x = 4 and 2x = 8. Sum and difference of these two 12, 4 respectively. Then difference between these two 8. Got answer.
(2)