Question

2. A positive number is 5 times another number if 21 is added to both the numbers,
then one of the new numbers becomes twice the other new number. What are the
numbers?​

Answer 1

❍ Let the another number be x respectively.

$\underline{\bigstar\:\boldsymbol{According\;to\;the\; Question:}}$⠀⠀

• Case – I) A Positive number is 5 times the another Number.

Therefore,

The Positive number = 5x

• Case – II) If 21 is added to Both the numbers, then one of the new number becomes twice the other new number.

Therefore,

• First number = (x + 21)
• Second Number = (5x + 21)

Now,

$:\implies\sf 5x + 21 = 2(x + 21) \\\\\\:\implies\sf 5x + 21 = 2x + 42 \\\\\\:\implies\sf 5x - 2x + 21 = 42\\\\\\:\implies\sf 3x + 21 = 42\\\\\\:\implies\sf 3x = 42 - 21\\\\\\:\implies\sf 3x = 21\\\\\\:\implies\sf x = \cancel\dfrac{21}{3}\\\\\\:\implies{\boxed{\underline{\frak{\purple{x = 7}}}}}\;\bigstar$

Hence,

• First number, x = 7
• Second number, 5x = 5(7) = 35

$\therefore{\underline{\textsf{Hence,\;the\: required\;numbers\;are\; \textbf{7 and 35}.}}}$

⠀⠀⠀⠀⠀

Answer 2

Given:

A positive number becomes 5 times another number

If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number.

To Find:

Both numbers

Solution:

Let the 1st number be = 5x

and 2nd number be = x

Now according to question:

--> If 21 is added to both numbers

1st number = 5x + 21

2nd number = x + 21

and

--> Then new numbers becomes twice the other new number.

--> 5x + 21 = 2 ( x + 21 )

--> 5x + 21 = 2x + 42

--> 3x = 21

--> x = 7

1st number = 5x = 5×7 = 35

2nd number = x = 7

Hence, required numbers are 35 and 7.