Question

A fraction's value is 4/5. When its numerator
is increased by 9, the new fraction equals
the reciprocal of the value of the original
fraction. Find the original fraction​

Answer 1

Answer :

16/20

Solution :

Let the numerator and the denominator of the original fraction be N and D respectively .

Also ,

It is given that , the value of original fraction is 4/5 .

Thus ,

=> N/D = 4/5

=> 5N = 4D ------(1)

Also ,

When its numerator is increased by 9, the new fraction equals the reciprocal of the value of the original fraction .

Thus ,

=> (N + 9)/D = 5/4

=> 4(N + 9) = 5D

=> 4N + 36 = 5D -------(2)

Now ,

Multiplying eq-(1) by 5 , we get ;

=> 5(5N) = 5(4D)

=> 25N = 20D -------(3)

Now ,

Multiplying eq-(2) by 4 , we get ;

=> 4(4N + 36) = 4(5D)

=> 16N + 144 = 20D --------(4)

From eq-(3) and (4) , we have ;

=> 25N = 16N + 144

=> 25N - 16N = 144

=> 9N = 144

=> N = 144/9

=> N = 16

Now ,

Putting N = 16 in eq-(1) , we get ;

=> 4D = 5N

=> 4D = 5•16

=> D = 5•16/4

=> D = 5•4

=> D = 20

Hence ,

The original fraction is 16/20 .

Answer 2

Answer:

hiii

purple u

have a great day

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