Question

The difference between two numbers is 8. If2 is added to the bigger number the result
will be three times the smaller number. Find the numbers.​

Answer 1

Given :-

• The difference between two numbers is 8. If 2 is added to the bigger number the result will be three times the smaller number

To find :-

• Required numbers

Solution :-

Let the bigger number be x then smaller number be y

• Difference between two numbers is 8.

→ x - y = 8 ----(i)

• 2 is added to the bigger number the result will be three times the smaller number

→ x + 2 = 3y

→ x - 3y = - 2 -----(ii)

Subtract both the equations

→ (x - y) - (x - 3y) = 8 - (-2)

→ x - y - x + 3y = 8 + 2

→ x - x - y + 3y = 10

→ 3y - y = 10

→ 2y = 10

→ y = 10/2

→ y = 5

Put the value of y in equation (i)

→ x - y = 8

→ x - 5 = 8

→ x = 8 + 5

→ x = 13

Hence,

• Bigger number = x = 13

• Smaller number = y = 5

Answer 2

Answer:

Let the Smaller No. be n and Greater No. be (n + 8)

• According to the Question :

⇒ Greater No. + 2 = 3 × Smaller No.

⇒ (n + 8) + 2 = 3 × n

⇒ n + 8 + 2 = 3n

⇒ n + 10 = 3n

⇒ 10 = 3n - n

⇒ 10 = 2n

• Dividing both by 2

⇒ n = 5

━━━━━━━━━━━━━━━━━

• Required Numbers :

◗ Smaller No. = n = 5

◗ Greater No. = (n + 8) = 13