Question

If x is the mean proportional between 12.8 and 64.8 and
y is the third proportional to 38.4 and 57.6, then 2x : y
is equal to:
12​

Answer 1

Given :-

• x is the mean proportional between 12.8 and 64.8.
• y is the third proportional to 38.4 and 57.6 .

To Find :-

• 2x : y = ?

Solution :-

we know that,

• Mean proportion of a and b = √(ab)

so,

→ x = Mean proportion of 12.8 and 64.8

→ x = √(12.8 * 64.8)

→ x = √(829.44)

→ x = 28.8

now,

→ The third proportional to 38.4 and 57.6 = y

so,

→ 38.4 : 57.6 :: 57.6 : y

→ Product of Extreme = Product of Means .

→ 38.4 * y = 57.6 * 57.6

→ y = (57.6 * 57.6) / 38.4

→ y = 86.4

therefore,

→ 2x : y

→ 2(28.8) : 86.4

→ 2(28.8) : 3(28.8)

→ 2 : 3 (Ans.)