Question

One number is three times the other number. If 15 is
added to both the numbers, then one of the new
numbers becomes twice that of the other number. The
sum of the numbers is -​

Answer 1

Let the one Number be X.

Then the other number = 3X

Five is added to both the numbers then the numbers becomes (X+5) and (3X+5)

According to question,

3X +5 = 2(X+5)

3X +5 = 2x +10

X = 5.

Therefore,

One Number = X = 5

And,

The other number = 3X = 3 × 5 = 15

3X-2X = 10-5

Answer 2

Solution :-

Let,

First number = x

Second number = y

According to the first condition :-

$\longrightarrow \sf x= 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............................(1)$

According to the second condition :-

$\longrightarrow \sf x+15 = 2(y+15 ) \\\\\longrightarrow x+15 = 2y+30 \\\\\longrightarrow x-2y = 30-15 \\\\\longrightarrow x-2y = 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............................(2)$

Substitute the value of x in eq (2),

$\longrightarrow \sf 3y- 2y = 15 \\\\\longrightarrow \bf y = 15$

Substitute y = 15 in eq (1),

$\longrightarrow \sf x = 3 \times 15 \\\\\longrightarrow \bf x = 45$

The two numbers are 45 and 15 .

Their sum = 45 + 15

                 = 60