Question

Find the Fraction which is equal to ½ when both its numerator and denominator are increased by 1 and which is equal to ⅔ when both are increased by 4.​

Answer 1

Answer:

Solution:

Suppose the Fraction be x/y

According to the conditions given in the Question,

⇒x+1/y+1 = ½ and

⇒x+4/y+4 = ⅔

⟹ 2x + 2 = y + 1 &

⟹ 3x + 12 = 2y + 8

⇒2x - y = -1 ....(i)

⇒3x - 2y = -4 ....(ii)

☯ Multiply the Equation:-

(i) by 2,

4x - 2y = -2 .......(iii)

☯ Subtracting Equation (ii) from equation (iii), :-

We have,

x = 2

☯ Substituting the value of x in equation no. (i) ,

We have,

2 × 2 - y = -1

.'. y = 4 + 1 = 5

Hence,

The Required Fraction,

⟹ 2/5