which number should be added 15,19 and 24 such that the resultant number are in continued proportion
Answers
Answer:
⁷
Step-by-step explanation:
Continued proportion : Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion.
Thus, if a, b and c are in continued-proportion, then
a,b,b,c are in proportion, that means
a : b : : b : c
⇒ Product of extremes = Product of means
⇒ a x c = b x b
⇒ a x c = b 2
Continued-proportion is also known as mean proportional .
If ‘b’ is a mean proportional between a and c then b 2 = ac.
Examples :
1) Find the mean proportional between 9 and 25.
Solution :
Let x be the mean proportional between 9 and 25.
⇒ x 2 = 9 x 25
⇒ x 2 = 225
⇒ x = 15
Hence, the mean proportional between 9 and 25 is 15.
-------------------------------------------------------------------------
2) ) Let x be the number added to 15, 19, ,24
5 + x/11 + x = 19 + x/37 + x
Applying componendo and dividendo rule,
5 + x + 11 + x/5 + x – 11 – x = 19 + x + 37 + x/19 + x – 37 – x
16 + 2x/- 6 = 56 + 2x/- 18
3(16 + 2x) = 56 + 2x
6x – 2x = 56 – 48
4x = 8
x = 2