Mean Proportional and Third Proportional MCQ Quiz - Objective Question with Answer for Mean Proportional and Third Proportional - Download Free PDF

Formula Used:

For 2 numbers a,b,

Mean proportion = √ab

Third proportion = b²/a

Calculation:

Mean proportion of 1.6 and 3.6 = √(1.6 × 3.6)

⇒ 2.4

The third proportion of 5 and 8,

64/5

Required ratio = (2.4 : 64/5) = 12 : 64

⇒ 3 : 16

∴ The required answer is 3 : 16.

Formula Used:

For 2 numbers a,b,

Mean proportion = √ab

Third proportion = b²/a

Calculation:

Mean proportion of 1.6 and 3.6 = √(1.6 × 3.6)

⇒ 2.4

The third proportion of 5 and 8,

64/5

Required ratio = (2.4 : 64/5) = 12 : 64

⇒ 3 : 16

∴ The required answer is 3 : 16.

Formula Used:

For 2 numbers a,b,

Mean proportion = √ab

Third proportion = b²/a

Calculation:

Mean proportion of 1.6 and 3.6 = √(1.6 × 3.6)

⇒ 2.4

The third proportion of 5 and 8,

64/5

Required ratio = (2.4 : 64/5) = 12 : 64

⇒ 3 : 16

∴ The required answer is 3 : 16.

Given:

The mean proportion of two numbers is 40.

Their third proportion is 320.

Formula used:

1. Mean proportion = √(a × b)

2. Third proportion = b²/a

Calculations:

Mean proportion = 40

⇒ √(a × b) = 40

⇒ a × b = 40² = 1600

Third proportion = 320

⇒ b²/a = 320

⇒ b² = 320 × a

From a × b = 1600:

⇒ b = 1600/a

Substitute b = 1600/a into b² = 320 × a:

⇒ (1600/a)² = 320 × a

⇒ 1600²/a² = 320 × a

⇒ 2560000/a² = 320 × a

⇒ 2560000 = 320 × a³

⇒ a³ = 2560000/320 = 8000

⇒ a = ∛8000 = 20

Substitute a = 20 into a × b = 1600:

⇒ 20 × b = 1600

⇒ b = 1600/20 = 80

Sum of the numbers = a + b = 20 + 80 = 100

∴ The correct answer is option (1).