Question

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained us 3/2. Find the rational number

Answer 1

ɢɪᴠᴇɴ :-

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained us 3/2.

Tᴏ ғɪɴᴅ :-

• Rational Number

sᴏʟᴜᴛɪᴏɴ :-

Let the rational number be x / y

then,

• According to 1st condition :-

➦ Denominator = Numerator + 8

➦ y = (x + 8) ---(1)

• According to 2nd Condition :-

$\implies \: \sf \frac{x + 17}{y - 1} = \frac{3}{2} \\ \\ \implies \: \sf 2(x + 17) = 3(y - 1) \\ \\ \implies \: \sf 2x + 34 = 3y - 3 \\ \\ \implies \: \sf 2x - 3y = - 34 - 3 \\ \\ \implies \: \sf 2x - 3y = - 37$

We get,

➦ (2x - 3y) = -37. ---(2)

Put the value of (1) in (2) , we get,

➮ 2x - 3y = -37

➮ 2x -3(8 + x) = 37

➮ 2x - 24 - 3x = -37

➮ -x = -37 + 24

➮ -x = -13

➮ x = 13

Put x = 13 in (1) ,we get,

➮ y = (x + 8)

➮ y = 13 + 8

➮ y = 21

Hence,

• Rational number is x/y = 13/21

Answer 2

Answer:

Rational number is 13/21

Explained below ↓

Step-by-step explanation:

Let the numerator be x ,

Denominator = x + 8

Fraction ₁ = x/x+8 ( Rational number )

New numerator = x + 17

New denominator = ( x + 8 ) - 1 = x + 7

Fraction ₂ = x + 17/x + 7

By the question,

x + 17/x + 7 = 3/2

By Cross-multiplying,

2( x + 17 ) = 3( x + 7 )

= 2x + 34 = 3x + 21 = 3x - 2x = 34 - 21

= x = 13

Rational number = x/x +8

= 13 / 13+8 = 13/21

Hope this helps.