Question

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator find the fraction

Answer 1

Answer:

The required fraction is $\frac{7}{15}$

Step-by-step explanation:

Let the fraction be $\frac{x}{y}$

As per given data,

$\frac{x-2}{y}=\frac{1}{3}$

3(x-2)=y

3x-y=6......................(1)

$\frac{x}{y-1}=\frac{1}{2}$

2x=y-1

2x-y=-1..................(2)

we solve (1) and (2)

3x-y=6......................(1)

2x-y=-1.....................(2)

(1)-(2) gives

x=7

put x=7 in (1) we get

21-y = 6

y = 21-6

y = 15

The required fraction is $\frac{7}{15}$

Answer 2

Answer:

fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator then fraction = 7/15

Step-by-step explanation:

Let say Fraction = N/D

A fraction becomes 1/3 when 2 is subtracted from the numerator

(N-2)/D = 1/3

=> 3N - 6 = D

=> 3N - D = 6  Eq 1

A fraction  becomes 1/2 when 1 is subtracted from the denominator

N/(D-1) = 1/2

=> 2N = D -1

=> 2N - D = -1   Eq 2

Eq 1 - Eq 2

N = 7

3* 7 - D = 6

=> D = 15

Fraction = N/D = 7/15