Question

16.6 is the mean proportional between two numbers x
and y and 48 is the third proportional of x and y. Find
the numbers.
(ICSE 2011)​

Answer 1

Answer:

The numbers are 3 and 12

Explanation:

Given numbers, x and y

Where, 6 is the mean proportion and 48 is the third proportion of x and y.

Now, from the first condition,

⇒ x : 6 : : 6 : y

⇒ x/6 = 6/y

⇒ xy = 6*6

⇒ xy = 36

∴ x = 36/y . . . . . (i)

Again, from the 2nd condition,

48 is continued as the third proportion.

∴ x : y : : y : 48

⇒ x/y = y/48

⇒ 48x = y² . . . . . . . (ii)

Substitute the value of eq. (i) we get,

⇒ 48 • 36/y = y²

⇒ 48 • 36 = y³

⇒ 1728 = y³

⇒ ∛1728 = y

⇒ 12 = y

∴ y = 12

Now, substitute the value of ‘y’ in eq. (ii) we get,

⇒ 48x = y²

⇒ 48x = 12*12

⇒ x = 144/48

⇒ x = 3

Hence, the number are 3 & 12