atalpanditgmat wrote:
A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?
A. (5^1/2 − 1)
B. (5^1/2 + 1) / 2
C. (5^1/2 + 1) / 4
D. (5^1/2 + 1) / (5^1/2 − 1)
E. (5^1/2 + 3) / (5^1/2 − 1)
Let N be the natural number...
Let N be divided into 2 parts p (larger part) and m (smaller part)
So, N = m+p........(i)
Also Given N/p = p/m
-> Nm = p^2 ......(ii)
Multiplying m on both sides of (i), we get
Nm = m^2 + pm
Putting value from (ii), we get
P^2 = m^2 + pm
Dividing both sides by m^2 , we get
(p/m)^2 = 1+ p/m
Let p/m = x
SO, x^2 = 1+x
X^2 - x - 1 = 0
\(x = (1+\sqrt{5})/2, (1-\sqrt{5})/2\)
Ratio must be +ve
So, x =\((1+\sqrt{5})/2\)
Answer B
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