Question

two numbers are in ratio 2:3 if 2 be subtracted from the first and 2 be added to the second, the ratio becomes 1:2 find the sum of the numbers
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Answer 1

Answer:

30

Step-by-step explanation:

let us take the numbers as 2x and 3x

so 2x-2 / 3x+2 = 1/2

= 4x-4 = 3x+2 [cross multiplication]

=> x = 6

so 2x + 3x = 5x = 5X6 = 30

Answer 2

• The sum of the numbers = 30.

Given :

• The ratio of the two numbers = 2 : 3.
• If 2 subtracted from the first and 2 added to the second number.
• The ratio after adding and subtracting = 1 : 2.

To Find :

• The sum of the numbers.

Solution :

Let,

The first number be 2x.

The second number be 3x.

We need to find the numbers.

First, we need to find the value of x.

According to the condition,

If 2 subtracted from first number.

⇒ 2x – 2

If 2 added to the second number.

⇒ 3x + 2

results become,

⇒ 1 / 2

That means,

⇒ 2x – 2 / 3x + 2 = 1 / 2

⇒ 2 ( 2x – 2 ) = 1 ( 3x + 2 )

⇒ 4x – 4 = 3x + 2

⇒ 4x – 3x = 2 + 4

⇒ 1x = 6

Therefore,

⇒ x = 6

So, the numbers are :

★ The first number.

⇒ 2x

⇒ 2 ( 6 )

⇒ 2 × 6

⇒ 12

★ The second number.

⇒ 3x

⇒ 3 ( 6 )

⇒ 3 × 6

⇒ 18

Hence, the numbers are 12 and 18.

Now, we have to find the sum of both numbers.

• First number + Second number

We have,

First number = 12

Second number = 18

⇒ 12 + 18

⇒ 30

Hence,

The sum of both the numbers is 30.