Question

THE DENOMINATOR OF A RATIONAL NUMBER IS GREATER THAN THE NUMERATOR BY 5. IF THE NUMERATOR IS INCREASED BY 11 AND THE DENOMINATOR IS DECREASED BY 3 . THE RESULT OBTAINED IS 5/2 FIND THE RATIONAL NUMBER

Answer 1

GIVEN

The denominator of a rational number is greater than the numerator by 5 . If the numerator is increased by 11 and the denominator is decreased by 3. The result obtained is 5/2

TO FIND

Find the rational number

SOLUTION

✞ Let the numerator be x

**According to the given condition**

✰The denominator of a rational number is greater than the numerator by 5

• x/x + 5

✰If the numerator is increased by 11 and the denominator is decreased by 3. The result obtained is 5/2

• x + 11/(x + 5) - 3 = 5/2

➥ x + 11/x + 5 - 3 = 5/2

➥ x + 11/x + 2 = 5/2

➥ 2(x + 11) = 5(x + 2)

➥ 2x + 22 = 5x + 10

➥ 2x - 5x = -22 + 10

➥ - 3x = - 12

➥ x = 12/3 = 4

Required rational number

= numerator/denominator

= x/x + 5

= 4/4 + 5 = 4/9

Hence, the required rational number is 4/9

Answer 2

Gɪᴠᴇɴ :-

THE DENOMINATOR OF A RATIONAL NUMBER IS GREATER THAN THE NUMERATOR BY 5. IF THE NUMERATOR IS INCREASED BY 11 AND THE DENOMINATOR IS DECREASED BY 3 . THE RESULT OBTAINED IS 5/2.

ᴛᴏ ғɪɴᴅ :-

• Rational Number

sᴏʟᴜᴛɪᴏɴ :-

➠ Let the numerator be x

And,

➠ Denominator be y

Then,

➠ Denominator = Numerator + 5

➡ y = ( x + 5 ) ---(1)

Now,

$\implies \: \frac{x + 11}{y - 3} = \frac{5}{2}$

Put y = (x + 5) in above equation , We get,

$\implies \: \frac{x + 11}{(x + 5) - 3} = \frac{5}{2} \\ \\ \implies \: 2(x + 11) = 5(x + 2) \\ \\ \implies \: 2x + 22 = 5x + 10 \\ \\ \implies \: 5x - 2x = 22 - 10 \\ \\ \implies \: 3x = 12 \\ \\ \implies \: x = \frac{12}{3} \\ \\ \implies \: x = 4$

Put x = 4 in (1) , we get,

➡ y = ( x + 5)

➡ y = 4 + 5

➡ y = 9

Hence,

• Rational number = x/y = 4/9