# 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 ?

Answer: Option

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 2*x* and *x* respectively.

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

9*x* = 36

*x* = 4.

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

Discussion:

45 comments Page 1 of 5.
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.

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)

Swamy said:
11 months ago

Let's assume 2 digit number is 10.

10x - 01x = 36,

9x = 36,

x = 4.

Coming to question; 1:2;

1x:2x.

1x4: 2x4.

4:8.

Then the answer is 8.

10x - 01x = 36,

9x = 36,

x = 4.

Coming to question; 1:2;

1x:2x.

1x4: 2x4.

4:8.

Then the answer is 8.

(17)

Maganizo Chithila said:
3 years ago

Ratio is 1:2

we will consider 1 and 2 as the numbers.

And have variable x after the subtracting.

then (21 -12)x=36.

Then 9x=36

And x=4 .

And have 2x for the second number which is 8.

the difference is 8-4 = 4.

the sum of 8+4 = 12.

Therefore the difference is 12-4 = 8.

we will consider 1 and 2 as the numbers.

And have variable x after the subtracting.

then (21 -12)x=36.

Then 9x=36

And x=4 .

And have 2x for the second number which is 8.

the difference is 8-4 = 4.

the sum of 8+4 = 12.

Therefore the difference is 12-4 = 8.

(11)

Sirjan said:
2 months ago

As ratio of the numbers is 1:2 and it's 2 digit number so possible numbers are only - 12, 24, 36 and 48.

Among those 48 and 84 (reversed 48) gives difference of 36.

So, the digit is 48.

The sum of digits, 8 + 4 = 12

Difference of digits, 8 - 4 = 4

Required difference. 12 - 4 = 8.

Among those 48 and 84 (reversed 48) gives difference of 36.

So, the digit is 48.

The sum of digits, 8 + 4 = 12

Difference of digits, 8 - 4 = 4

Required difference. 12 - 4 = 8.

(6)

Bhargavi said:
3 years ago

From 3rd question,we can say x-y=4.

We have to find diff of ( sum of digits n diff of digits).

(X+y)-(x-y)=0.

X+y=4.

From 2 equations,we get X=4, sub X value then y=0,

So 2 numbers are 40 and 04,

Sum is 44,diff is 36.

So, diff is 44 - 36 = 8.

We have to find diff of ( sum of digits n diff of digits).

(X+y)-(x-y)=0.

X+y=4.

From 2 equations,we get X=4, sub X value then y=0,

So 2 numbers are 40 and 04,

Sum is 44,diff is 36.

So, diff is 44 - 36 = 8.

(6)

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.

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)

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.

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)

Chinnadurai said:
9 years ago

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.

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)

Anju said:
6 years ago

Since they have mentioned the word "difference" in the problem so the answer will be 8 .From the 1st part of the question we can find that X-Y=4, also they have mentioned X/Y=1/2 hence Y=2X;

Therefore X~2X=4;hence X=4;Y=8;

So, the answer is :(4+8)~(4~8)=8.

Therefore X~2X=4;hence X=4;Y=8;

So, the answer is :(4+8)~(4~8)=8.

(1)

Jonsihay said:
9 years ago

The Problem should be re-stated specially on the aspect of the ratio.

It should "NOT JUST BE" 'if the ratio between the digits of the number is 1:2. But it should be restated as 'if the ratio between the unit's and ten's digits of the number is 1:2.

Then if that's ok, I think reliably be solvable!

It should "NOT JUST BE" 'if the ratio between the digits of the number is 1:2. But it should be restated as 'if the ratio between the unit's and ten's digits of the number is 1:2.

Then if that's ok, I think reliably be solvable!

(1)

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