Question

If the numerator of a fraction is increased by 1, its value becomes 3/4. If its denominator is increased by 2, its value becomes 1/2. Then (i) Write the equations for the given conditions , (ii) Find the fraction.

Answer 1

Let’s assume that the numerator and denominator of the fraction be x and y respectively. Therefore, the fraction is x/y

According to given condition’s,

x = y – 4,

x – y = − 4

and y + 1 = 8(x – 2)

y + 1 = 8x – 16

8x – y = 1 + 16

8x – y = 17

Therefore, we have two equations

x – y = -4     —————-(i)

8x – y = 17         ——————(ii)

Subtracting the second equation from the first equation, we get

(x – y) – (8x – y) = – 4 – 17

x − y − 8x + y = −21

−7x = −21

−7x = −21

x = 21/7 = 3

Substituting the value of x in the , we have

3 – y = – 4

y = 3 + 4 = 7

Hence the fraction is 3/7