This is a basic question from ML aggarwal book of class 10th, chapter 7, ratio and proportion., ICSE board
We have to find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
Question 11, exercise 7.2
Solution:
Consider a and b as the two numbers
It is given that 28 is the mean proportional
a: 28 :: 28: b
We get
ab = 282 = 784
Here a = 784/b …… (1)
We know that 224 is the third proportional
a: b :: b: 224
So we get
b2 = 224a ….. (2)
Now by substituting the value of a in equation (2)
b2 = 224 × 784/b
So we get
b3 = 224 × 784
b3 = 175616 = 563
b = 56
By substituting the value of b in equation (1)
a = 784/56 = 14
Therefore, 14 and 56 are the two numbers.