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?
Answers
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}}}⟶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}}}⟶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}}}⟶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
\begin{gathered} \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\end{gathered}
4x−3y+1=0
4x−2y−6=0
(−)(+)(+)
−y+7=0
⟹−y+7=0
⟹−y=−7
Taking - ( minus ) common on both sides
⟹−(y)=−(7)
−(minus)getscancelled
⟹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 )
Value of x = 5
value of y = 7