# 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 |

10*x*^{2} + 8 + 18*x* = 80 + *x*^{2}

9*x*^{2} + 18*x* - 72 = 0

*x*^{2} + 2*x* - 8 = 0

(*x* + 4)(*x* - 2) = 0

*x* = 2.

Discussion:

42 comments Page 1 of 5.
Manav Pawar said:
1 year ago

Anyone, please explain this to get it.

(1)

Ishu said:
2 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.

(30)

Yash said:
3 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)

Soumi said:
4 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.

(11)

Pema dechen said:
4 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.

(2)

Tamilarasi said:
4 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.

(8)

KRISHNA GUPTA said:
5 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:
5 years ago

I am not understanding this answer.

Ganga Bhavani said:
6 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.

(1)

Mitun C Das said:
6 years ago

Answer is absolutely 24. I agree.

(1)

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