Question

If 1 is added to both mumenator or
denominator,a fraction becomes 3/4.If 3 is subtract from both numenator or denominator the fraction becomes 1/2.What is the fraction?​

Answer 1

ans .is of this que. is

y = 7

x= 5

Answer 2

Given : -

If 1 is added to both numerator and denominator , a fraction becomes as 3/4 .

If 3 is subtracted from both numerator and denominator the fraction becomes 1/2 .

Required to find : -

• Original fraction ?

Solution : -

If 1 is added to both numerator and denominator , a fraction becomes as 3/4 .

If 3 is subtracted from both numerator and denominator the fraction becomes 1/2 .

We need to find the original fraction .

So,

For these questions we need to use the concepts of linear equations in 2 variables .

Let,

The numerator of the fraction be x

The denominator of the fraction be y

Consider Statement - 1

If 1 is added to both numerator and denominator , a fraction becomes as 3/4 .

So,

According to which ;

➺ x + 1/y + 1 = 3/4

Cross Multiplication on both sides

➺ 4 ( x + 1 ) = 3 ( y + 1 )

➺ 4x + 4 = 3y + 3

➺ 4x - 3y = 3 - 4

➺ 4x - 3y = - 1

4x - 3y + 1 = 0 $\longrightarrow{\tt{\bf{ Equation - 1}}}$

Consider this as equation - 1

Similarly,

Consider statement - 2

If 3 is subtracted from both numerator and denominator the fraction becomes 1/2 .

So,

According to which ;

➺ x - 3/ y - 3 = 1/2

Cross multiplication on both sides

➺ 2 ( x - 3 ) = 1 ( y - 3 )

➺ 2x - 6 = y - 3

➺ 2x - y = - 3 + 6

➺ 2x - y = 3

2x - y - 3 = 0 $\longrightarrow{\tt{\bf{ Equation - 2}}}$

Consider this as equation - 2

Consider equation - 2

➺ 2x - y - 3 = 0

Multiply with 2 on both sides

➺ 2 ( 2x - y - 3 ) = 2 ( 0 )

4x - 2y - 6 = 0 $\longrightarrow{\tt{\bf{ Equation - 3}}}$

Consider this as equation - 3

Now,

We need to solve these 2 equations simultaneously .

Using Elimination method let's eliminate one of the variable to simplify our calculations .

Subtract equation 1 & equation 3

$\sf 4x - 3y + 1 = 0 \\ \sf 4x - 2y - 6 = 0 \\ \underline{ \sf ( - )( + )( + ) \: \: \: \: \: \: \: \: \: \: \: \: } \\ \underline{ \sf \: \: \: \: \: \: \: \: \: \: - y + 7 = 0} \\ \\ \implies \rm - y + 7 = 0 \\ \\ \implies \rm - y = - 7 \\ \\ \textsf{ Taking - ( minus ) common on both sides} \\ \\ \implies \rm - (y) = - (7) \\ \\ \tt - \: (minus) \: gets \: cancelled \\ \\ \implies \tt y = 7$

Hence,

• Value of y = 7

Substitute the value of 5 in equation 1

➺ 4x - 3y + 1 = 0

➺ 4x - 3y = - 1

➺ 4x - 3 ( 7 ) = - 1

➺ 4x - 21 = - 1

➺ 4x = - 1 + 21

➺ 4x = 20

➺ x = 20/4

➺ x = 5

Hence,

• Value of x = 5

Therefore,

Original fraction = x/y = 5/7

( Since, numerator is considered to be as x and denominator is considered to be as y )

Hence Solved ! ✓