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

Method 1)

Let the -

• one number be "M"

A positive number is 5 times the another number.

So,

Another number = 5M

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

After adding 21 to both numbers, number becomes -

• One number = M + 21
• Another number = 5M + 21

According to question,

⇒ 2(M + 21) = 5M + 21

⇒ 2M + 42 = 5M + 21

⇒ 2M - 5M = 21 - 42

⇒ - 3M = - 21

⇒ 3M = 21

⇒ M = 7

So,

• One number = M

⇒ 7

• Another number = 5M

⇒ 5(7)

⇒ 35

•°• Numbers are 7 and 35.

Method 2)

Let the -

• One number be M
• Another number be N.

A positive number is 5 times the other.

→ M = 5N ____ (eq 1)

If 21 is added on both sides, then the one number becomes twice the other number.

• One number = M + 21
• Another number = N + 21

According to question,

→ M + 21 = 2(N + 21)

→ M + 21 = 2N + 42

→ 5N + 21 = 2N + 42 [From (eq 1)]

→ 5N - 2N = 42 - 21

→ 3N = 21

→ N = 7

Substitute value of N in (eq 1)

→ M = 5(7)

→ M = 35

•°• Numbers are 35 and 7.

Answer 2

$\huge\sf{Answer:-}$

Given 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.

To Find:-

We have to find what are the numbers.

Hence:-

Let x be the one number and let y be the other number.

Equation (1) – [x = 5y]

Therefore:-

• 1st number (x + 21)
• 2nd number (y + 21)

Given question:-

$\sf = x+ 21 = 2(y + 21) \\ \sf = x + 21 = 2y + 42 \\ \sf = 5y + 21 = 2y + 42 \\ \sf = 5y - 2y = 42 - 21 \\ \sf = 3y = 21 \\ \sf ⟶y = 7$

Adding values:-

$\sf ⟶x = 5(7) \\ \sf ⟶x = 35$

[.•.] Therefore, 35 and 7 are the numbers.

– NayanShreyas