When k is added to each of 11, 27, 20 and 44, then the numbers so obtained in this order, are in proportion. What is the mean proportional between (k+2) and (3k-5)?

Correct option is D

Given :
When k is added to 11, 27, 20, 44, the resulting numbers are in proportion.

So,
(11+k) : (27+k) = (20+k) : (44+k)

Formula Used :
If a : b = c : d then
​$$a \times d = b \times c$$​​

Mean proportional between two numbers (a) and (b) is
​$$\sqrt{ab}$$​​

Solution :

(11+k)(44+k) = (27+k)(20+k)

4$$84 + 55k + k^2 = 540 + 47k + k^2$$​

55k - 47k = 540 - 484

8k = 56

k = 7
Now find mean proportional between

(k+2) and (3k-5)

k+2 = 9, 3k-5 = 16

Mean proportional
​$$\sqrt{9 \times 16} = \sqrt{144} =$$​12