Question

9. Two numbes are in the ratio of 2:3. If 15 added to both the number, then the ratio between two numbers becomes the numbers become 11/14. find the greater number.
(1) 29
(2) 27
(3) 29
(4) 30​

Answer 1

Given :

Two numbes are in the ratio of 2:3. If 15 added to both the number, then the ratio between two numbers becomes the numbers become 11/14.

To Find :

The greater number.

Solution :

Analysis :

Here we have to take a common ratio. Then forming a equation we can find the greater number.

Explanation :

Let the common ratio be “x”.

• 2x
• 3x

After adding 15,

• 2x + 15
• 3x + 15

It is said that if 15 is added to both the numbers, then the ratio between two numbers becomes the numbers become 11 : 14.

☯ According to the question,

⇒ (2x + 15)/(3x + 15) = 11/14

By cross multiplying,

⇒ 14(2x + 15) = 11(3x + 15)

⇒ 28x + 210 = 33x + 165

Transposing 28x to RHS and 165 to LHS,

⇒ 210 - 165 = 33x - 28x

⇒ 45 = 5x

⇒ 45/5 = x

⇒ 9 = x

∴ x = 9.

The numbers :

• 2x = 2 × 9 = 18
• 3x = 3 × 9 = 27

⇒ 27 > 18

So,

Your answer is option (2).

The greater number is 27.

Verification :

LHS :

⇒ (2x + 15)/(3x + 15)

• Putting x = 9,

⇒ (2(9) + 15)/(3(9) + 15)

⇒ (18 + 15)/(27 + 15)

⇒ 33/42

Dividing both the numerator and denominator by 3,

⇒ 11/14

∴ 11/14.

RHS :

∴ 11/14.

∴ LHS = RHS.

• Hence verified.

Answer 2

Answer:

Step-by-step explanation: