Question

the numerator and the denominator of a fraction are each reduced by 1 the resultant fraction equals 2/3 if they are reduced by 3 each the resultant fraction equals to 1/2 find the fraction​

Answer 1

Answer:

Let the fraction be

b

a

.

Therefore,

b−3

a+2

=1

a+2=b−3

a−b=−5 .......(1)

Also,

b+3

a−2

=

8

3

8a−16=3b+9

8a−3b=25

Solving these equations, we get,

a=8 and b=13

Answer 2

Answer:

${\huge{\boxed{\red{\mathscr{AnSwEr}}}}}$

Let the fraction be $\huge{\boxed{\sf \frac{x}{y} }}$

Now According to The Question

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

Cross - multiply both sides

→3(x-1)=2(y-1)

→3x-3=2y-2

→3x-2y=1

→3x=1+2y

$→x = \frac{1 + 2y}{3} - - - - - (1)$

Now take second Condition

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

Now Do the same

→2(x-3)=1(y-3)

→2x-6=y-3

→2x-y=3------------(2)

Put the value of x in eq (2)

$2 \times ( \frac{1 + 2y}{3} ) - y = 3$

$\frac{2 + 4y}{3} - y = 3$

$\frac{2 + y}{3} = 3$

2+y=9

y=7

Now put the value of (y) in eq (2)

2x-7=3

2x=10

x=5

So the fraction is

${\huge{\boxed{\red{\mathscr{ \frac{5}{7} }}}}}$