Question

if we add 1 in both numerator and denominator of a fraction,
it becomes 4 /5 and if we subtract 5 from both numerator and denominator it becomes 1/ 2 .find the fraction.​

Answer 1

hope it will help you

Answer 2

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$\frac{7}{9}$

step-by-step explanation:

Let,

the given fraction be $\frac{p}{q}$ where q≠ 0

Now,

A.T.Q

if we add 1 in both numerator and denominator of the fraction,

it becomes 4 /5

=> (p+1)/(q+1) = 4/5

=> 5(p+1) = 4(q+1)

=> 5p + 5 = 4q + 4

=> 5p - 4q = -1

=> 4q -5p = 1 ..............(i)

Now,

again,

if we subtract 5 from both numerator and denominator it becomes 1/ 2

=> (p-5)/(q-5) = 1/2

=> 2(p-5) = (q-5)

=> 2p - 10 = q -5

=> 2p - q = 5

multiplying this eqn with 4,

we get,

=> 8p - 4q = 20 .............(ii)

Now,

adding eqn (i) and (ii),

we get,

3p = 21

=> p = 21/3

=> p = 7

putting this value in eqn (ii),

we get,

=> 8×7 - 4q = 20

=> 4q = 56- 20

=> 4q = 36

=> q = 36/4

=> q = 9

HENCE,

the fraction is $\frac{7}{9}$