Question

A string is cut into two parts. The ratio of the lengths
of the string and the smaller part is six times the ratio
of the lengths of the smaller and the larger parts. Find
the ratio of the lengths of the larger and smaller parts
of the string.
(A) 2:1 (B) 3:1 (C) 4:1 (D) 5:1
C​

Answer 1

Answer:

a) 2:1

Step-by-step explanation:

latest let the string be 1 unit of length

shorter piece =x

longer piece=1-x

ratio of string to smaller part = 1/x

ratio smaller part to the larger part = x/(1-x)

1/x = 6(x/1-x)

6x^1=1-x

6x^2+x-1=0

(3x-1)(2x+1)=0

x=1/3 or x=-1/2, the last answer makes no sense

so, smaller is 1/3 larger is 2/3

ratio of larger to smaller

=(2/3)/(1/3)

= 2:1