Question

One number is 3 times another number. If 5 is added to both the numbers, then one of the new numbers becomes twice that of the other new number. Find the numbers.

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• One number is 3 times another number.

Let assume that

• First number = x

So,

• Second number = 3x

Further given that,

If 5 is added to both the numbers, then one of the new numbers becomes twice that of the other new number.

So,

• First number = x + 5

• Second number = 3x + 5

According to statement

$\rm \: 3x + 5 = 2(x + 5)$

$\rm \: 3x + 5 = 2x + 10$

$\rm \: 3x - 2x = 10 - 5$

$\bf\implies \:x = 5$

So,

• First number = 5

• Second number = 3x = 3 × 5 = 15

$\rule{190pt}{2pt}$

Basic Concept Used :-

1. Read the problem carefully and understand what is given and what to find.

2. Understand the relationship between known and unknown quantities.

3. Assign the variable to unknown quantity.

4. Frame the equation by using unknown variable and given information.

5. Solve the problem to get the value of known variable.

Answer 2

Question :-

One number is 3 times another number. If 15 is added to both the numbers, then one of the new numbers becomes twice that of the other new number. Find the numbers.

Solution:-

Let one number be x .

Second number =3 x

After adding 15 to both, the new numbers are: x+15 and 3 x+15

Now,

$\[ \begin{array}{l} \rm 2(x+15)=3 x+15 \\ \\ \rm2 x+30=3 x+15 \\ \\ \rm 30-15=3 x-2 x \\ \\ \rm 15=x \\ \\ \boxed{\red{ \rm x=15}} \end{array} \]$

Numbers are x=15 and 3 x=3(15)=45.

Hence, the numbers are 15 and 45 .