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.
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raushan6198:
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step-by-step explanation:
Let,
the given fraction be 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
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