Let the numbers be x and y.
According to question,
The ratio of two numbers is 4:7.
⇒ x/y = 4/7
⇒ 7x = 4y
∴ 7x - 4y = 0 ........................(1)
Again According to question,
If each of those numbers increased by 30, their ratio will become 5:8
(x + 30) / (y + 30) = 5/8
⇒ 8(x + 30) = 5(y + 30)
⇒ 8x + 240 = 5y + 150
⇒ 8x - 5y = -90 ..........................(2)
Multiply 5 with equation (1) , we will get.
35x - 20y = 0 ..................(3)
Multiply 4 with equation (2), we will get.
32x - 20y = -360 ............(4)
Subtracts the Equation (4) from Equation (3). we will get,
35x - 20y - (32x - 20y) = 0 - (-360)
⇒ 35x - 20y - 32x + 20y = 360
⇒ 3x = 360
⇒ x = 120
Put the value of x in equation (1) to get the value of y.
7x - 4y = 0
⇒ 7(120) - 4y = 0
⇒ 840 - 4y = 0
⇒ 4y = 840
⇒ y = 210
∴ Average of the numbers = (x + y)/2
put the vale of x and y.
∴ Average of the numbers = (120 + 210)/2
∴ Average of the numbers = 330/2
∴ Average of the numbers = 165
