Question

if the numerator of a fraction is increased by 2 and the denominator by 1 becomes 5 / 8 if numerator and denominator of a fraction is increased by 1 the fraction becomes 1 /2 find the fractions​

Answer 1

Step-by-step explanation:

Let the numerator is = x

Denominator is = y

Fraction = x/y

According to the question,

Numerator is increased by 2 = x+2

Denominator is increased by 1 = y+1

Then, x+2/y+1 = 5/8

=> 8×(x+2) =5×(y+1)

=> 8x + 16 =5y + 5

=> 8x - 5y = 5 - 16

=> 8x - 5y = - 11 - - - - - - (1)

Again,

Numerator is increased by 1= x +1

Denominator is increased by 1 = y + 1

x + 1/y + 1= 1/2

=>2 (x+1) =1(y + 1)

=> 2x + 2 = y + 1

=> 2x - y = 1 - 2

=> 2x - y = - 1 - - - - - - -(2)

From equation (1)×1 - (2)× 5, we get

8x - 5y = - 11 - - - - - -(3)

10 x - 5y = - 5 - - - - - (4)

——————————————

8x - 10x = - 11-(-5)

=>- 2x = - 11 + 5

=> - 2x = - 6

=> x = - 6/-2

=> x = 3

Now, putting the value of x in equation (2),

2x - y = - 1

=>2 × 3 - y = - 1

=> 6 - y = - 1

=> 6 + 1 = y

=> 7 = y

=> y = 7

Hence,

• Numerator (x) = 3
• Denominator (y) = 7
• Fraction = x/y = 3/7 ANS.