Question

The numerator of a fraction is 4 less than its denominator. if the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes 8 times its numerator. find the freaction

Answer 1

Let the numerator be x and denominator be x+4

When the numerator is decreased by 2,that is x-2 and denominator is increased by 1,that is x+4+1=x+5, the denominator becomes:

denominator=8*numerator=8(x-2)=8x-16

That is,  x+5=8x-16

Subtracting x from both the sides,

5-x+x=8x-x-16

5=7x-16

Adding 16 to both the sides,

5+16=7x-16+16

21=7x

7x=21

Dividing both the sides by 7

7x/7=21/7

x=3

Hence, numerator is 3 and denominator is 3+4=7

Therefore, the fraction is 3/7



Hope This Helps!

Answer 2

Answer:

Let the numerator be x & denominator be y

Fraction = numerator/denominator = x/y

ATQ

CASE 1 :

x = y - 4

x- y = - 4 …………..(1)

CASE 2 :

8(x - 2) = y + 1

8x - 16 = y + 1

8x - y = 17………... (2)

On Subtracting eq (2) from (1)

x - y = - 4

8x - y = 17

(-) (+) (-)

----------------

-7x = -21

x = 21/7

x = 3

Put x = 3 in eq 1,

x - y = - 4

3 - y = - 4

y = 3 + 4 = 7

y = 7 

x = 3

y = 7

Fraction = x/y = 3/7

Hence, the fraction is 3/7