Aptitude - Problems on Numbers - Discussion

I have assumed that X ,Y, Z are the three numbers and their positions are 100X+10Y+Z
now;

According to the que;
X+Y+Z=10---> (1)
and
X+Z=Y -------> (2).

From eq 1 and eq 2.

We get;
Y=5 ----> (3)
from eq2 and eq 3.
we get;
X+Y=5----->(4)
now from here, it is sure that number would have 5 digit in its middle.

a/c to que
(100X+ 10Y+Z) +99= 100Z+10Y+X
99= 99Z-99X
1= Z-X------------> (5)

from eq 4 and eq 5;
we get X=2.
Z=3.

So the number is 253 the answer.

Let me explain guys,

x+y+z=10 (given) --> 1
y(MIDDLE DIGIT)= x+z (given) -->2
substitute equation 2 in 1.
y+y =10,
2y=10,
y=5.
(100x+50+z) - (100z+50+x) = 99 (difference between the number and the reversed one)
100x+50+z-100z-50-x = 99,
99x-99z= 99,
99(x-z) =99,
x-z=1
w.k.t x+z=5
By simultaneous equation x=3;
3+z=5
z=2;
352 - 253 =99.

Another way to solve this is,

Let the digits be x,y,z.

Given-
x+y+z=10.

And
y = x + z.

Then=> y+y=2y=10=>y=5
Number is either 253 or 352.
The number is increased by 99,when reversed.
Therefore the answer is 253.

It's quite simple first see it says the middle digit is equal to the sum of the other digits so in the options (option elimination method).

145 isn't the answer because 1+5 isn't equal to 4
370 isn't the answer because 3+0 isn't equal to 7.
253 and 352 one among these will be the answer. Because 2+3 or 3+2 will be equal to 5
Next, it's given the number is increased by 99 if the digits are reversed so it's obviously 253 because of 253+99=352.

Let the number be 100x +10y +z.
Now x+y+z = 10 (given),
also y=x+z (given),

--> y+(x+z) = y+y = 2y = 10.
--> y=5.

Now 5= 1+4 or 2+3 .
also z>x (using the third given statement)
So the number can be 154 or 253.
reverse the numbers and subtract,
451-154 = 297,
352- 253 = 99.
Therefore, here the answer can only be 253 i.e option B.

The sum of 3 digits = a + b + c.
a + b + c = 10( is given).

Middle num is = sum of the other two.

b = (a + c).
then a + b + c = 10,
(a + c) + b = 10,
b + b = 10,
2b = 10,
b = 5.

So, if a = 3, b = 5, c = 2 then abc = 352.
or a = 2, b = 5, c = 3 then abc= 253.

1) 352 - 253 = 99.
2) 253 - 352 =-99.

In the problem, they gave 99 only so the first step is right.

Lets Suppose three digits are a,b,c
Than a+b+c=10
But b=a+c (given)
a+c+b=10
(a+c)+b=10
b+b=10
b=10/2=5
so the middle digit is 5
so a=3or2 and c=3or2 (3+2=5)
thats why the number is either 253 or 352
But the actual no is 99 less than the reverse no.
352-253=99

: . so the no is 253

If middle digit is 5, then the sum of other two digits is also 5.
So, Why don't we consider (1, 4 or 4,1)?
As 1+4 or 4+1 is also 5.

Please explain.

@Anagha.

For these type of questions we have to go with the options. Because there are so many 3 digit numbers like that (132 etc....) but we don't have those options here.

Please explain once for simple method.