Aptitude - Problems on Numbers - Discussion
Discussion Forum : Problems on Numbers - General Questions (Q.No. 5)
5.
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Answer: Option
Explanation:
Let the ten's and unit digit be x and | 8 | respectively. |
x |
Then, | 10x + | 8 | + 18 = 10 x | 8 | + x | ||
x | x |
10x2 + 8 + 18x = 80 + x2
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2.
Discussion:
42 comments Page 1 of 5.
Ishu said:
3 years ago
Possibilities of getting a product 8 is 24 or 42.
If 18 is added to 42, it gives 60 --> the reversing condition is not met.
Else if you add 18 to 24 --> 18+24 = 42, the reverse of 24.
Hence the answer is 24.
If 18 is added to 42, it gives 60 --> the reversing condition is not met.
Else if you add 18 to 24 --> 18+24 = 42, the reverse of 24.
Hence the answer is 24.
(58)
Soumi said:
5 years ago
Two digits let be x and y
So, two digit no. =10x+y.
Given, xy=8.
=>y=8/x or x=8/y...(1).
So, (10x+y) +18=10y+x
=>9x+18=9y
=>x+2=y----(2).
Putting the Value of x from eqn 1 in eqn 2.
8/y-y = -2.
y^2-2y-8 = 0.
y^2-4y+2y-8 = 0.
y(y-4) +2(y-4) = 0.
y = 4/-2, y can't be a negative integer.
So y = 4.
And x = 2.
So, no. is 24.
So, two digit no. =10x+y.
Given, xy=8.
=>y=8/x or x=8/y...(1).
So, (10x+y) +18=10y+x
=>9x+18=9y
=>x+2=y----(2).
Putting the Value of x from eqn 1 in eqn 2.
8/y-y = -2.
y^2-2y-8 = 0.
y^2-4y+2y-8 = 0.
y(y-4) +2(y-4) = 0.
y = 4/-2, y can't be a negative integer.
So y = 4.
And x = 2.
So, no. is 24.
(27)
Tamilarasi said:
5 years ago
The two digits are 2, 4.
24+18(add 18),
The answer is 42,
Reverse the 42.
Then the final answer is 24.
24+18(add 18),
The answer is 42,
Reverse the 42.
Then the final answer is 24.
(14)
Manav Pawar said:
2 years ago
Anyone, please explain this to get it.
(3)
Yash said:
4 years ago
Why X is taken as in the tenth position while 8/X taken as in-unit?
We could have taken X in unit and 8/X in tenth place?
Please explain me.
We could have taken X in unit and 8/X in tenth place?
Please explain me.
(3)
Pema dechen said:
5 years ago
Well the solution is such that;
Given condition:
xy = 8.
xy*18 = yx.
Now, let tens place be x and ones place be 8/x (using 1st condition).
Using second condition we will have;
10x+8/x+18=80/x+x.
Calculating we get;
x=2 and y=4.
Hence, combining we have and 2,4 i.e,24.
Given condition:
xy = 8.
xy*18 = yx.
Now, let tens place be x and ones place be 8/x (using 1st condition).
Using second condition we will have;
10x+8/x+18=80/x+x.
Calculating we get;
x=2 and y=4.
Hence, combining we have and 2,4 i.e,24.
(3)
Ganga Bhavani said:
7 years ago
First let us consider the the number is xy.
Then the number value = 10x+y.
Given that if we add 18 to the number then it would be equal to reverse of the number(yx which value is 10y+x).
i.e 10x+y+18 = 10y+x.
10x+y+18-10y-x = 0.
9x-9y+18 = 0.
x-y+2 = 0 ------------------------------------------------- (1).
But we know product of digits is 8 i.e xy = 8.
then x = 8/y.
so substitute x = 8/y in equation 1.
then 8/y -y + 2 = 0.
i.e 8-y^2+2y = 0.
y^2-2y-8 = 0.
y^2 - 4y-2y -8 = 0.
y(y-4)+2(y-4) = 0.
y= -2 or 4.
we take positive y, then y= 4.
then x= 8/y = 8/4 = 2.
So the number is xy i.e 24.
Then the number value = 10x+y.
Given that if we add 18 to the number then it would be equal to reverse of the number(yx which value is 10y+x).
i.e 10x+y+18 = 10y+x.
10x+y+18-10y-x = 0.
9x-9y+18 = 0.
x-y+2 = 0 ------------------------------------------------- (1).
But we know product of digits is 8 i.e xy = 8.
then x = 8/y.
so substitute x = 8/y in equation 1.
then 8/y -y + 2 = 0.
i.e 8-y^2+2y = 0.
y^2-2y-8 = 0.
y^2 - 4y-2y -8 = 0.
y(y-4)+2(y-4) = 0.
y= -2 or 4.
we take positive y, then y= 4.
then x= 8/y = 8/4 = 2.
So the number is xy i.e 24.
(3)
KRISHNA GUPTA said:
6 years ago
Lets number is xy;
Given xy=8; -----> (1)
10x + y + 18 = 10y+x.
y-x = 2 ----> (2).
Put y=8/x in (1)
So x^2+2x-8=0;
the root is 2,-4
x=2 so y is 4.
So the number is xy= 24.
Given xy=8; -----> (1)
10x + y + 18 = 10y+x.
y-x = 2 ----> (2).
Put y=8/x in (1)
So x^2+2x-8=0;
the root is 2,-4
x=2 so y is 4.
So the number is xy= 24.
(2)
Jason said:
6 years ago
I am not understanding this answer.
(2)
Sam said:
8 years ago
Can anyone explain it in another way?
(1)
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