Aptitude - Problems on Numbers - Discussion

Mitali: Good Explanation from you, thanks.

Two digits x&y
x:y=1:2
x=k
y=2k
two numbers 10x+y&10y+x
10x+y=10k+2k=12k
10y+x=20k+k=21k
diff=9k=36
k=4
numbers 12k=48
21k=84
sum of dgts=12
diff of dgts=4
ans=sum-diff=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

Let's the digits are x & y.

The ratio between them is x:y = 1:2.

So y=2x.

Hence y is ten digit no.
According to statement,

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

(y+x)-(y-x) = (2x+4)-(2x-4).

= (8+4)-(8-4).

= 12-4 = 8.

In the first condition, we get,
10x+y-(10y-x) = 36.

So, 9x-9y = 36.
By solving this we get x-y = 4. Thats all.

Can anyone explain why do we take (y+x)-(y-x) in the last step rather than 10x+y-(10y-x) ?

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.

Why are you taking (10*2x+x) - (10+2x) = 36? Please explain it.

Assume the 2 digit number be 84 and by interchanging the digits we get 48.

Difference 84-48 = 36.
Sum = 4+8= 12.
Difference = 8-4 = 4.

Difference between sum & diff = 12-4 = 8.

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.