If x : y = (frac{1}{4} : frac{3}{8}) and y : z = (frac{1}{3} : frac{4}{9}), find x : z
-
A.
2:3 -
B.
3:4 -
C.
3:8 -
D.
1:2
Correct Answer: Option D
Explanation
(frac{x}{y}) = (frac{1}{4} div frac{3}{8}) = (frac{1}{4} times frac{8}{3}) = (frac{2}{3})
(frac{y}{z}) = (frac{1}{3} div frac{4}{9}) = (frac{1}{3} times frac{9}{4}) = (frac{3}{4})
But,
x = (frac{2}{5}T_1), y = (frac{3}{5}T_1)
y = (frac{3}{7}T_2), z = (frac{4}{7}T_2)
Using y = y
(frac{3}{5}T_1) = x = (frac{3}{7}T_2)
(frac{T_1}{T_2}) = (frac{3}{7}) x (frac{5}{3}) = (frac{15}{21})
(T_1 = 15) and (T_2 = 21)
Thus , x = (frac{2}{5}) x 15 = 6
y = (frac{3}{5}) x 15 = 9
y = (frac{3}{7}) x 21 = 9
z = (frac{4}{7}) x 21 = 12
Hence; x : z = 6 : 12
= 1 : 2