Question

*The denominator of a number is 9 more than its numerator. If 5 is added to the denominator, it becomes thrice the numerator. Which of the following is the original number?*
1️⃣ 2/7
2️⃣ 7/16
3️⃣ 28/37
4️⃣ 12/21

Answer 1

Answer-

(2) 7/16

$\star$ SOLUTION:

Given:

• The denominator of a number is 9 more than its numerator
• If 5 is added to the denominator, it becomes thrice the numerator.

To be found:

The original fraction =?

Now,

Let the numerator be x

So, from the given question we can get the value of denominator = 9 more than the numerator = (x+9)

Also,

According to the question,

When 5 is added to the denominator, then it becomes thrice of the numerator.

⇒ (x+9) + 5 = 3x

⇒ x + 9 + 5 = 3x

⇒ x + 14 = 3x

⇒ 14 = 3x - x

⇒ 14 = 2x

⇒ 14 ÷ 2 = x

⇒ 7 = x

So,

The value of the numerator = x = 7

And the value of the denominator = (x+9) = 7+9 = 16

So,

The required fraction is 7/16

Answer 2

Answer:

(2) 7/16

Step-by-step explanation:

Assume that the numerator is x and denominator is y. So, fraction is x/y.

The denominator of a number is 9 more than its numerator.

As per given condition,

→ y = 9 + x ...................(1)

If 5 is added to the denominator, it becomes thrice the numerator.

As per given condition,

→ (y + 5) = 3x

→ 9 + x + 5 = 3x

→ 14 = 2x

→ x = 7

Substitute value of x in (1)

→ y = 16

Hence, the original fraction = x/y = 7/16.