If (x+y):(x−y)=5:2, find the value of
x−4y
4x+5y
.
- A43/5
- B-5/43
- C-43/5
- D5/43
Solution & Step-by-step Explanation
Given:
x−y
x+y
=
2
5
Cross-multiplying to find the relation between x and y:
2(x+y)=5(x−y)
2x+2y=5x−5y
2y+5y=5x−2x
7y=3x
y
x
=
3
7
Let x=7k and y=3k. Substitute these values into the required expression:
x−4y
4x+5y
=
7k−4(3k)
4(7k)+5(3k)
=
7k−12k
28k+15k
=
−5k
43k
=−
5
43
x−y
x+y
=
2
5
Cross-multiplying to find the relation between x and y:
2(x+y)=5(x−y)
2x+2y=5x−5y
2y+5y=5x−2x
7y=3x
y
x
=
3
7
Let x=7k and y=3k. Substitute these values into the required expression:
x−4y
4x+5y
=
7k−4(3k)
4(7k)+5(3k)
=
7k−12k
28k+15k
=
−5k
43k
=−
5
43