The ratio of third proportional to 21 and 42 and mean proportional to 16 and 49 is ?

Ques - The ratio of third proportional to 21 and 42 and mean proportional to 16 and 49 is ?

(a) 3 : 1

(b) 2 : 3

(c) 1 : 3

(d) 4 : 3

Solution - 

Let,

The third proportion = x.

so,

21, 42 and x be in continued proportion.

Therefore,

21 : 42 :: 42 : x

21/42 = 42/x

1/2 = 42/x

x = 84

Thus,

The third proportion is 84.

Now,

Let,

Mean proportion = y

so,

16, y and 49 be in continued proportion.

Therefore,

16 : y :: y : 49

16/y = y/49

16 × 49 = y²

y² = 16 × 49

y = squareroot of 16 × 49

y = (16 × 49)½

y = 4 × 7

y = 28

Thus,

The Mean proportion is 28.

Therefore,

Requried ratio = 84 : 28

= 3 : 1

The ratio of third proportional to 21 and 42 and mean proportional to 16 and 49 is 3 : 1.

Hence,

The correct answer is option (a) 3 : 1.

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