Question

A positive number is five times another no. if 21 is added to both number. then, one of the new no. becomes twice the other no.

Answer 1

let the numbers be x and y
According to the given condition x=5y
given that if 21 is added to both the numbers one is twice of other
21+ x=2(y+21)
21+x=2y+42
x-2y=21 substitute x=5y
5y-2y=21
3y=21
y=7,x=5y
x=35
Thus the numbers are 7 and 35

Answer 2

Let another number be 'a'.

so now let another positive number be '5a'.

Question asks us to add 21 to both the numbers. So let's add 21 to both the numbers.

So the numbers will become --- "a+21" and " "5a+21".

Now the problem lies in the next part of the question.

which number becomes twice of which number ?

the number which is bigger can be assumed to be twice of the other number. but now how we will come to know which number is bigger ?

so let's take an example ..

let's take 2. if you add 1 to 2 then it becomes "2+1". This means "2+1" is greater than "2".

In the Same way,

5a+21 is greater than just "a+21". ( because in 5a+21, there are 5 a's.)

So now we can easily assume "5a+21" to be twice of "a+21".

5a+21 = 2( a+21)

5a+21 = 2a + 42

3a = 21

a = 7

so that positive number is 5a meaning that number is 35. answer.

Should you have any doubts let me know in the comment section.