Question

two numbers are in the ratio of 3:5 if 5 is subtracted from each other, they become in the ratio of 1:2 , find the numbers​

Answer 1

Given :-

• Two numbers are in the ratio of 3:5 if 5 is subtracted from each other, they become in the ratio of 1:2

To find :-

• Find the numbers

Solution :-

• Two numbers are in the ratio = 3 : 5

Let the first number be 3x and second number be 5x

• 5 is subtracted from each other, they become in the ratio of 1:2

According to question

→ 3x - 5/5x - 5 = ½

→ 2(3x - 5) = 5x - 5

→ 6x - 10 = 5x - 5

→ 6x - 5x = 10 - 5

→ x = 5

Hence,

• x = 5

Therefore,

• Required numbers

• First number = 3x = 15

• Second number = 5x = 25

Answer 2

Answer :

The two numbers are 15 and 25

Explanation :

According to the question :

Let the two numbers be ' a ' and ' b '

⟶ a : b = 3 : 5

⟶ a / b = 3 / 5

⟶ b = 5a / 3 ...... [ 1 st Equation ]

➤ Then, ( 5 is subtracted ) :

⟶ a - 5 / b - 5 = 1 / 2 ⋆ { cross multiply ✖ }

⟶ 2 ( a - 5 ) = 1 ( b - 5 )

⟶ 2a - 10 = b - 5

⟶ 2a - b = 10 - 5

⟶ 2a - b = 5 ...... [ 2 nd Equation ]

➤ Putting ( b = 5a / 3 ) value in 1 st Equation :

⇛2a - ( b = 5a / 3 ) = 5

⇛2a - ( 5a / 3 ) = 5 ⋆ { LCM = 3 }

⇛2a × 3 - 5a / 3 = 5

⇛6a - 5a / 3 = 5

⇛1a / 3 = 5

⇛a = 5 × 3

⇛a = 15

➤ Putting ( a = 15 ) value in 2 nd Equation :

⇛2a - b = 5

⇛2 ( 15 ) - b = 5

⇛30 - b = 5

⇛b = 30 - 5

⇛b = 25

Hence, Proved !!