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:

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SSC CGL Previous Paper 66 (Held On: 3 March 2020 Shift 2)
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  1. 3 : 4
  2. 1 : 2
  3. 2 : 3
  4. 4 : 5

Answer (Detailed Solution Below)

Option 3 : 2 : 3
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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If x is the mean proportional between 12.8 and 64.8, then

12.8 : x : : x : 64.8

⇒ 12.8/x = x/64.8

⇒ x2 = 12.8 × 64.8

⇒ x = √[16 × 0.8 × 0.8 × 81]

⇒ x = 4 × 0.8 × 9

If y is the third proportional to 38.4 and 57.6, then

38.4 : 57.6 : : 57.6 : y

⇒ 38.4/57.6 = 57.6/y

⇒ y = (57.6 × 57.6)/38.4

⇒ y = 86.4

Now,

2x : y = 2 × 4 × 0.8 × 9 : 86.4 = 2 : 3

Short Trick :

Mean Proportional x = √12.8 × 64.8 = 28.8

Third proportional y = (57.6 × 57.6)/38.4 = 86.4

Now,

2x : y = 2 × 28.8 : 86.4 = 2 : 3
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