Question

A positive number is 4 times another number. When 12 is added to both the numbers, the first new number
is 2 1/2 times the other new number. Find the original numbers
​

Answer 1

${\huge{\boxed{\sf{\color{lime}{★}}{Required\: \: Answer :}}}}$

To Solve:

• Find the original numbers

Given:

• A number is 4 times another number.

• When 12 is added to both the numbers, the first new number is 2 1/2 times the other new number.

Solⁿ:

• Assume the no.s
• Make eqⁿ according to question.
• Put them equal, find the values
• Put the values in the assumed no.s, and get the Original numbers.

» Let one number be = x

» Let another number be = 4x

When 12 is added:-

» 1ˢᵗ number = 12+x

» 2ⁿᵈ number = 12 + 4x

When Added:-

12 + 4x = 2 1/2 (12+x)

Solve:

$12 + 4x = 2 \frac{1}{2} (12 + x) \\ \\ 12 + 4x = \frac{5}{2} (12 + x) \\ \\ 12 + 4x = \frac{{ \cancel{60}}}{ \cancel{2}} + \frac{5}{2}x \\ \\ 4x - \frac{5}{2}x = 30 - 12 \\ \\ \frac{8x - 5x}{2} = 18 \\ \\ \frac{3x}{2} = 18 \\ \\ 3x = 18 \times 2 \\ \\ 3x = 36 \\ \\ x = \frac{36}{3} \\ \\{ \boxed{ \color{lime}{ x = 12}}}$

Now, the numbers are :-

X = 12

4x = 4×12 = 48

So, the numbers are 12 and 48

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