Aptitude - Problems on Numbers - Discussion

Let's not look into the options to solve this. Let's solve from the scratch--
The product of 2 digits is 8:-

1 * 8 = 8
2 * 4 = 8
4 * 2 = 8
8 * 1= 8.

So, the number has to be any of the above-given numbers i.e 18 or 24 or 42 or 81.

Now, add 18 to all the above 4 numbers, only 24 will be reversed after adding 18. => 24 = 42 (reversed).

So, 24 is the answer.

How can solve like this manner 8+18 = 24?

8+18 = 26. It's wrong. The product of the number is 8 not that number.

First we have to check with the options then only we find answer easily.

Here the first condition is that the multiple of that two digit number is 8.
Then we check all the options. Given four options satisfying the 1st condition.

Now go to 2nd condition, i.e if 18 is added to that two digit number the answer will be reversed.
So we can check through all the options then we get 24 is the correct option.

i.e 2*4 = 8.
24 + 18 = 42.

Hence the 2 conditions are satisfied.

Let the ten's and unit digit be x and 8/x because on multiplying x*8/x we get 8. That's what is actually said at the first line of the question.

Now, suppose let's unit digit be 8/x and ten's digit be x. Now, the number becomes 10 * x + 8/x (let us consider this equation as equation number 1)

According to the question, given that
10 * x + 8/x + 18 = 10 * 8/x + x.

Further Solving by taking L.C.M on both sides we get the statement a 10x^2+8+18x = 80+x^2 (the sign (^) here denotes square of that number).

9x^2 +18x-72=0.

Take 9 as common from above equation, you'll get,
x^2 +2x-8 = 0.
x^2+4x-2x-8 = 0.
x(x+4)-2(x+4) = 0.
(x+4)(x-2) = 0.

Hence
x = 2 (since x = -4 cannot be taken becoz the digit is negative).

Now put x=2 in above equation number 1

Thus 10*x+8/x becomes
=10*2+8/2 (since x=2)
=20+4
=24
Hence the required answer is 24...
Any doubt plz ask ....!!

Two digits=x & y so two digit no = 10x+y.
Product of digits is x*y = 8.

So (10x+y)+18 = 10y+x.
i.e x-y = -2......(1).
as x*y=8 so x = 8/y.

Hence equation (1) becomes 8/y-y = -2......(2).
Solving equation(2) we get y = 2.

Putting y=2 in equation (1) we get x = 4.
So the two digited number xy = 42.

So please tell me how answer comes to 24.
Please correct me if I am wrong?

Answer is absolutely 24. I agree.

The sum of five numbers is 18, their average is 3. 6 and their difference is 1. What are the numbers?

Can anyone tell me the answer?

Hi @Gopinath.

How 8+18 = 24?

I think its 26.

xy = 8
10x + y + 18 = 10y = x
9x - 9y + 18 = 0
x-y = -2
8/y - y = -2
So by solving above equation we get y = 4,
by putting y=4 in xy=8 so we get x = 2.
So the original no. is 10x+y = 24.

Could anyone please provide the shortcut method?