# 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.
Ramya said:
1 decade ago

Hi I could not understand this problem. Can anyone explain this more clearly please?

(1)

Pavithra said:
1 decade ago

I get the answer as 16.

Diff in digits: (x+y)-(x-y)

=2y

=2(2x)

=4x.

Finding the value of x we get, x=4;

So ans = 4(4) = 16.

Diff in digits: (x+y)-(x-y)

=2y

=2(2x)

=4x.

Finding the value of x we get, x=4;

So ans = 4(4) = 16.

Sikha said:
1 decade ago

It can't b (x+y) - (x-y).

Rather it could be (10x +y) - (10y + x).

Rather it could be (10x +y) - (10y + x).

(1)

Sravanthi said:
1 decade ago

Hi I can't understand this problem. Any more explnation please.

(1)

Nathi said:
1 decade ago

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

((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

(2)

Santosh said:
1 decade ago

Why we have to take 2x in units place rather than x ? can any one explain.

Nagendra said:
1 decade ago

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

Hence the answer is 8.

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

Hence the answer is 8.

Shalini said:
1 decade ago

Why are we choosing 2x?

Mitali said:
1 decade ago

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

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

Virendra said:
1 decade ago

In question diff is given i.e. 36 and ratio is 1:2

We just find out such a pair without calculating.

We just find out such a pair without calculating.

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