1) Which number should be subtracted from 13, 25 and 55 such that resultant numbers are in continued proportion.
Answers
Answer:
5 should be subtracted from each number 13,25 and 55 so that resultant numbers are in continued proportion
Step-by-step explanation:
Let the number to be subtracted be x.
Therefore 13−x, 25−x, 55−x are in continued proportion.
We know that If a:b::b:c, then a,b,c are in continued proportion, and c is the third proportional of a and b.
= (b)^{2}(b)
2
= ac
= (25-x)^{2}=(13-x)*(55-x)(25−x)
2
=(13−x)∗(55−x)
Applying Identities we get
= a^{2} -50a+625 = a^{2}-68a+715a
2
−50a+625=a
2
−68a+715
=a^{2} -a^{2}-50a+68a = 715-625a
2
−a
2
−50a+68a=715−625
= 18a = 90
= a = 90/18
= a = 5
Therefore 5 needs to be subtracted from 13,25,55 such that they are in continued proportion.
Verification
= (13-5),(25-5),(55-5)
= 8,20 and 50
=8:20::20:50
As we know product of means (20 and 20) is equal to product of extremes (8 and 50).
20*20 = 8*50
400=400
LHS=RHS
I this will help you.