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If x : y = $\frac{1}{4} : \frac{3}{8}$ and y : z = \...

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

View answer & explanation

Correct answer is D

$\frac{x}{y}$ = $\frac{1}{4} \div \frac{3}{8}$ = $\frac{1}{4} \times \frac{8}{3}$ = $\frac{2}{3}$

$\frac{y}{z}$ = $\frac{1}{3} \div \frac{4}{9}$ = $\frac{1}{3} \times \frac{9}{4}$ = $\frac{3}{4}$

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

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