The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 1, the fraction
becomes 2/3Find the fraction.
Answers
Step-by-step explanation:
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.
HOPE THIS WILL HELP YOU...
Let the numerator and denominator of a fraction be x and y.
Required Fraction = numerator/denominator = x/y
1st Equation
⇒ x = y - 4
⇒ x- y = - 4 ……..(i)
2nd Equation
⇒ 8(x - 2) = y + 1
⇒ 8x - 16 = y + 1
⇒ 8x - y = 1....... (ii)
On Subtracting eq (ii) from (i)
⇒ -7x = -21
⇒ x = 21/7
⇒ x = 3
Putting x value in Eq (i)
⇒ x - y = - 4
⇒ 3 - y = - 4
⇒ y = 3 + 4 = 7
⇒ y = 7
The required fraction is 3/7.
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