Question

If x-30 is mean proportion to 35 and x+40, what is x​

Answer 1

Answer:

Question:

When x is added to each of 2, 3, 30 35 then the numbers obtained in this order, are in proportion. What is the mean proportional between (x + 7) and (x - 2)?

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Options:

4

7

6

5

Correct Answer: Option 3 (Solution Below)

Solution:

Calculation:

Let x is added to each of 2, 3, 30 and 35 to make numbers in proportion

(2 + x) / (3 + x) = (30 + x) / (35 + x)

Using dividend and componendo

(2 + x + 3 + x) / (2 + x - 3 - x) = (30 + x + 35 + x) / (30 + x - 35 - x)

⇒ (5 + 2x) / (-1) = (65 + 2x) / (-5)

⇒ 5(5 + 2x) = 65 + 2x

⇒ 25 + 10x = 65 + 2x

⇒ 10x - 2x = 65 - 25

⇒ 8x = 40

⇒ x = 40/8

⇒ x = 5

Mean proportional between (x + 7) and (x - 2)

√(x + 7)(x - 2) = √(5 + 7)(5 - 2) = √(12 × 3) = √36 = 6

Short trick

Mean proportional between (x + 7) and (x - 2) = √(x + 7)(x - 2)

Put the value of x = 1, 2, 3, 4, 5 …….., So that the number become a perfect square

So, put x = 5

⇒ √(5 + 7)(5 - 2)

⇒ √(12 × 3) = √36 = 6

Answer 2

Step-by-step explanation:

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