Two numbers are in the ratio 5:4 if 27 is added to each of them the ratio becomes 8:7 find the number
Answers
Solution
Given:-
- Two numbers are in the ratio 5:4
- 27 is added to each of them the ratio becomes 8:7
Find:-
- There are two number
Explanation
Let,
- First number be = x
- Second number be = y
A/C to question
(Two numbers are in the ratio 5:4 )
==> x : y = 5:4
==> x/y = 5/4
==> 4x - 5y = 0 ----------------equ(1)
And,
(27 is added to each of them the ratio becomes 8:7)
==> (27+x):(27+y) = 8:7
==> (27+x)/(27+y) = 8/7
==> 7.(27+x) = 8.(27+y)
==> 7x - 8y = 216 - 189
==> 7x - 8y = 27--------------------equ(2)
multiply by 7 in equ(1) & 4 in equ(2)
- 28x - 35y = 0
- 28x - 32y = 108
______________Sub. it's
==> (-35y + 32y) = -108
==> -3y = -108
==> y = -108/(-3)
==> y = 36
keep value in equ(1)
==>4x - 5*36 = 0
==> 4x = 180
==> x = 180/4
==> x = 45
Thus
- Value of first number (x) = 45
- Value of second number (y) = 36
__________________
Answer:
45 and 36
Step-by-step explanation:
Let the two numbers be 5x and 4x
According to Question,
5x + 27 = 8y
= 5x - 8y = - 27------------ eq 1
4x + 7y = -27
= 4x - 7y = -27 -------------eq2