Question

The denominator pf a rational number. is greater than its numerator by 5. If the numerator is increased by 11 and the denominator is descreased by 3 , the numerator obtained is 5/2 . Find the rational number​

Answer 1

• Answer •

‣ Rational number = 4/9

• Explanation •

Given information,

The denominator of a rational number is greater than it's numerator by 5. If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained is 5/2. Find the rational number.

• Denominator = Numerator + 5
• If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained = 5/2

Let,

• Numerator of rational number be x
• So, it's denominator will be (x + 5)

According to the Question,

• If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained = 5/2

Therefore,

➻ (x + 11)/(x + 5 - 3) = 5/2

➻ (x + 11)/(x + 2) = 5/2

By cross multiplication,

➻ 2(x + 11) = 5(x + 2)

➻ 2x + 22 = 5x + 10

➻ 2x - 5x = 10 - 22

➻ -3x = -12

➻ x = -12/-3

➻ x = 12/3

➻ x = 4

• Hence, numerator of the required rational number is 4.

Now,

➻ Denominator = Numerator + 5

➻ Denominator = x + 5

Putting value of ‘x’ in above eqⁿ,

➻ Denominator = 4 + 5

➻ Denominator = 9

• Hence, denominator of the required rational number is 9.

So,

• Rational number •

➻ Numerator/Denominator

➻ 4/9

• Hence, the required rational number is 4/9.

Verification,

• If the numerator is increased by 11 and the denominator is decreased by 3, the number obtained = 5/2

Therefore,

➻ (x + 11)/(x + 5 - 3) = 5/2

➻ (x + 11)/(x + 2) = 5/2

Putting value of ‘x’ in above eqⁿ,

➻ (4 + 11)/(4 + 2) = 5/2

➻ 15/6 = 5/2

➻ 5/2 = 5/2

➻ LHS = RHS

Hence, Verified ✔

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