Question

The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator
are increded by 3, then they are in the ratio 2:3. Deturmine the fraction.
​

Answer 1

Step-by-step explanation:

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$\bf \huge \: \: Question\: \:$

• The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator
• are increded by 3, then they are in the ratio 2:3.

_______________________________

$\bf \huge \: \: Given\: \:$

• The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator

• the numerator and denominator are increded by 3,
• they are in the ratio 2:3. Deturmine the fraction.

_______________________________

$\bf \huge \: \: To\: Find\:$

• Deturmine the fraction.

Let the numerator be x and denominator be

$\bf \: \ y. A/Q\:$

$\bf \: x + y = 4 + 2x \:$

$\bf \: → - x + y = 4 ... (1) \:$

multiplying each term by 2,

$\bf \:2x-2y= -8 .... (2)\:$

Also,

$\bf \: (x+3) / (y+3) = 2 / 3 \:$

$\bf \:→ 3x - 2y = -3 ........ (3) \:$

Subtracting (2) from (3)

$\bf \red{_\frac{3x - 2y = -3}{ 2x-2y= -8}= X = 5}$

→ x = 5 and by putting this in (1)

$\bf \: - x + y = 4\:$

$\bf \:-5+y=4\:$

$\bf \:y = 4+5=9\:$

we can get $\bf \red{y=9}\:$

Hence,

the fraction is$\bf \red{ 5 / 9}$

Answer 2

Question:

The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator

are increded by 3, then they are in the ratio 2:3. Deturmine the fraction.

Answer:

The given fraction will be $\frac{5}{9}$

Solution:

Let n be the numerator and d be the denominator.

Given,  

The sum of the given n and d is equal to twice the numerator plus 4, i.e.

$n + d = 2n + 4$

$n + s - 2n - 4 = 0$

$-n + d = 4$

$n - d = -4 .........(1)$

From given, the numerator n and the denominator d must be increased by 3 to get the ratio 2:3

$\frac{n+3}{d+3} = \frac{2}{3}$

$3n + 9 = 2d + 6$

$3n - 2d = 6 - 9$

$3n - 2d = -3 ...........(2)$

From equations (i) and (ii), we get,

$(i) × 3 \implies 3n - 3d = -12$

$(ii) \implies 3n - 2d = -3$

Solving (i) and (ii) we get,

$n - d = -4$

$n - 9 = -4$

$n = -4 + 9$

$n = 5$

∴ The given fraction is $\frac{n}{d} = \frac{5}{9}$