Question

The numerator of a fraiton ic 4 lecc than the nenominator. If 1 ic annen to both itc numerator ann nenominator, it beiomec ½. Finn the fraiton.

Answer 1

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.

Answer 2

Correct Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and numerator, it becomes ½.

Find out

Find the fraction

Solution

★Let the denominator be x then its numerator be (x - 4)

*According to the given condition*

‡ If 1 is added to both its numerator and numerator, it becomes ½.

➙ (x - 4) + 1/x + 1 = ½

➙ x - 4 + 1/x + 1 = ½

➙ x - 3/x + 1 = ½

➙ 2(x - 3) = x + 1

➙ 2x - 6 = x + 1

➙ 2x - x = 6 + 1

➙ x = 7

Hence,

• Required fraction
• Numerator/Denominator
• x-4/x = 3/7

$\rule{200}3$

Another method

★ Let the numerator be x then its denominator be y

*According to the given condition*

‡ Numerator of a fraction is 4 less than the denominator

• x = y - 4 ---(i)

‡ 1 is added to both its numerator and numerator, it becomes ½.

• x + 1/y + 1 = ½

➙ 2(x + 1) = y + 1

➙ 2x + 2 = y + 1

➙ 2x - y = 1 - 2

➙ 2x - y = - 1----(ii)

✑ Substitute the value of x in eqⁿ (ii)

➙ 2x - y = - 1

➙ 2(y - 4) - y = - 1

➙ 2y - 8 - y = - 1

➙ y - 8 = - 1

➙ y = 8 - 1 = 7

✑ Putting the value of y in eqⁿ (i)

➙ x = (y - 4)

➙ x = 7 - 4 = 3

Hence,

• Required fraction
• Numerator/denominator
• 3/7

$\rule{200}3$