Question

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

Given:-

• 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

To Find:-

• The New numbers.

Now,

Let the another number be "x"

Atq

→ First Number = 5x

Now, Atq again

→ x + 21 = 5x + 21

→ 2 ( x + 21 ) = 5x + 21

→ 2x + 42 = 5x + 21

→ 2x - 5x = 21 - 42

→ - 3x = - 21

→ 3x = 21

→ x = 21/3

→ x = 7.

Therefore, The Value of x is 7.

→ First Number = 5x → 5 × 7 = 35

→ Another Number = x = 7.

The Numbers are 35 and 7 Respectively.

VERIFICATION:-

if 21 is added to both the numbers then one of the new numbers becomes twice the other new

→ 7 + 21 = 35 + 21

→ 2 ( 7 + 21 ) = 35 + 21

→ 14 + 42 = 35 + 21

→ 56 = 56.

VERIFIED ✔️

Answer 2

Answer:

Let the first number be n and second number be 5n respectively.

• According to the Question :

• If 21 is added to both the numbers then one of the new numbers becomes twice the other new number.
• As 5n is already Greater, Hence Other Number will be Twice of this.

⇒ Twice of First Number = Second Number

⇒ 2 × (n + 21) = (5n + 21)

⇒ 2n + 42 = 5n + 21

⇒ 42 - 21 = 5n - 2n

⇒ 21 = 3n

• Dividing both term by 3

⇒ n = 7

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• Required Numbers :

◗ First Number = n = 7

◗ Second Number = 5n = 5(7) = 35

∴ Hence, Numbers are 7 and 35.