Question

if 2 is added to the numerator and denominator it becomes 9/10 and of 3 is subtract ted from the numerator and denominator becomes 4/5.Find the fraction ​

Answer 1

Solution

Given :-

• if 2 is added to the numerator and denominator it becomes 9/10
• 3 is subtract ted from the numerator and denominator becomes 4/5

Find :-

• These fraction

Explanation

Let,

• Numerator be = x
• Denominator be = y

A/C to question,

(if 2 is added to the numerator and denominator it becomes 9/10)

➡ (x+2)/(y+2) = 9/10

➡ 10*(x+2) = 9*(y+2)

➡10x - 9y = 18 - 20

➡ 10x - 9y = -2 ________(1)

Again,

(3 is subtract ted from the numerator and denominator becomes 4/5)

➡ (x - 3)/(y-3) = 4/5

➡5*(x-3) = 4*(y-3)

➡ 5x - 4y = 15 - 12

➡ 5x - 4y = 3 _________(2)

Multiply by 5 in equ(1) & 10 in equ(2)

➡ 50x - 45y = -10 ______(3)

➡ 50x - 40y = 30 ______(4)

Subtract equ(3) & equ(4)

➡ -45y + 40y = -10 - 30

➡ -5y = -40

➡ y = 40/5

➡y = 8

keep value of y in equ(2)

➡ 5x - 4*8 = 3

➡5x = 3 + 32

➡5x = 35

➡x = 35/5

➡x = 7

Hence

• Fraction will be (x/y) = 7/8

_________________

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• If 2 is added to the numerator and denominator it becomes 9/10

• If 3 is subtracted from the numerator and denominator it becomes ⅘.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The fraction.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the numerator be x

And denominator be y

According to the 1st condition :-

$\rm \longrightarrow\dfrac{x + 2}{y + 2} = \dfrac{9}{10}$

By cross multiplication:-

$\rm \longrightarrow{10(x + 2)} = {9(y + 2)}$

$\rm \longrightarrow{10x + 20} = {9y + 18}$

$\rm \longrightarrow{10x - 9y} = { 18 - 20}$

$\rm \longrightarrow{10x - 9y} = { - 2} .......(i)$

According to the 2nd condition :-

$\rm \longrightarrow\dfrac{x - 3}{y - 3} = \dfrac{4}{5}$

By cross multiplication:-

$\rm \longrightarrow{5(x - 3)} = {4(y - 3 )}$

$\rm \longrightarrow{5x - 15} = {4y - 12}$

$\rm \longrightarrow{5x - 4y} = { -12+15}$

$\rm \longrightarrow{5x - 4y} = { 3} .......(ii)$

Multiply equation (ii) with 2

→ 2(5x - 4y = 3)

→ 10x - 8y = 6

Subtract equation (i) from (ii) eliminate x

→ -8y + 9y = 6 + 2

→ y = 8

Substitute y = 8 in equation (ii)

→ 5x - 4y = 3

→ 5x - 4(8) = 3

→ 5x - 32 = 3

→ 5x = 3 + 32

→ 5x = 35

→ x = 7

Therefore:-

The numerator = x = 7

The denominator = y = 8

Hence:-

$\underline{\boxed{ \bf \purple{\leadsto The \: fraction \: = \frac{7}{8}} }}$