Question

Ratio of two numbers is 3:8. On adding 5 to both numbers, the ratio becomes 2:5. Which is the smaller number out of the two? ​

Answer 1

Answer :-

Let the numbers be 3x and 8x.

Adding 5 to both numbers :-

Numbers = 3x + 5 and 8x + 5

According to the question :-

→ 3x + 5 : 8x + 5 = 2 : 5

→ 3x + 5 / 8x + 5 = 2 / 5

→ 5 ( 3x + 5 ) = 2 ( 8x + 5 )

→ 15x + 25 = 16x + 10

→ 16x - 15x = 25 - 10

→ x = 15

Numbers are -

• 3x = 3 × 15 = 45
• 8x = 8 × 15 = 120

Smaller number = 45

Answer 2

A N S W E R :

• The smaller number out of the two is 45.

Given :

• Ratio of two numbers is 3 : 8

• After adding 5 to both numbers ratio becomes 2 : 5

To find :

• Find the smaller number ?

Solution :

• Let one number be x and other number be y

=> First number/Second number = 3/8

=> x/y = 3/8

=> 8x = 3y

=> x = 3y/8 (equation 1)

• Now adding 5 to both numbers

• One number = x + 5

• Other number = y + 5

• New ratio = 2 : 5

=> (x + 5)/(y + 5) = 2/5

=> 5(x + 5) = 2(y + 5)

=> 5x + 25 = 2y + 10

=> 5(3y/8) - 2y = 10 - 25

=> 15y - 16y/8 = -5

=> -y = -15 × 8

=> y = 120

Substituting the values, y in equation (1)

=> x = 3 × 120/8

=> x = 360/8 = 45

Hence,

• The smaller number out of the two is 45.