Question

the numerator of a rational number is 8 less than its denominator if the numerator is increased by 2 and the denominator is decreased by 1 the number obtained is 1 upon 2 find the number​

Answer 1

ɢɪᴠᴇɴ :-

The numerator of a rational number is 8 less than its denominator if the numerator is increased by 2 and the denominator is decreased by 1 the number obtained is 1 /2 .

Tᴏ ғɪɴᴅ :-

• Rational Number

sᴏʟᴜᴛɪᴏɴ :-

Let the rational number be x / y

then,

According to 1st Condition :-

➦ Numerator = Denominator - 8

➦ x = (y - 8) . ----(1)

According to 2nd Condition :-

$\implies\tt \: \frac{x + 2}{y - 1} = \frac{1}{2} \\ \\ \\ \implies \tt \: 2(x + 2) = 1(y - 1) \\ \\ \\ \implies \tt \: 2x + 4 = y - 1 \\ \\ \\ \implies \tt \: 2x - y = - 4 - 1 \\ \\ \\ \implies \tt \: 2x - y = - 5$

We get,

➦ 2x - y = -5 .---(2)

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

➮ 2x - y = -5

➮ 2(y - 8) - y = -5

➮ 2y - 16 - y = -5

➮ y = -5 + 16

➮ y = 11

Put y = 11 in (1) , we get,

➮ x = y - 8

➮ x = 11 - 8

➮ x = 3

Hence,

• Rational Number is x/y = 3/11