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If p : q = $\frac{2}{3}$ : $\frac{5}{6}$ and q : r = \(\...

If p : q = $\frac{2}{3}$ : $\frac{5}{6}$ and q : r = $\frac{3}{4}$ : $\frac{1}{2}$ , find p : q : r

A.

12 : 15 : 10

B.

12 : 15 : 16

C.

10 : 15 : 24

D.

9 : 10 : 15

View answer & explanation

Correct answer is A

If p : q = $\frac{2}{3}$ : $\frac{5}{6}$ , then the sum S1 of ratio = $\frac{2}{3}$ + $\frac{5}{6}$ = $\frac{9}{6}$

If q : r = $\frac{3}{4}$ : $\frac{1}{2}$ , then the sum S2 of ratio = $\frac{3}{4}$ + $\frac{1}{2}$ = $\frac{5}{4}$

Let p + q = T1, then

q = ( $\frac{5}{6} \div \frac{9}{6}$ )T1 = ( $\frac{5}{6} \times \frac{6}{9}$ )T1 = $\frac{5}{9}$ T1

Again, let q + r = T2, then

q = ( $\frac{3}{4} \div \frac{5}{4}$ )T2 = ( $\frac{3}{4} \times \frac{4}{5}$ )T2 = $\frac{3}{5}$ T2

Using q = q

$\frac{5}{9}$ T1 = $\frac{3}{5}$ T2

5 x 5T1 = 9 x 3T2

$\frac{T_1}{T_2}$ = $\frac{9 \times 3}{5 x 5}$ = $\frac{27}{25}$

Giving that, T1 = 27 and T2 = 25

P = ( $\frac{2}{3} \div S_1$ )T1 = ( $\frac{2}{3} \div \frac{9}{6}$ )T1

= ( $\frac{2}{3} \times \frac{6}{9}$ )27 = 12

q = ( $\frac{5}{6} \div S_1$ )T1 = ( $\frac{5}{6} \div \frac{9}{6}$ )T1

= ( $\frac{5}{6} \times \frac{6}{9}$ )27 = 15

and r = ( $\frac{1}{2} \div S_2$ )T2 = ( $\frac{1}{2} \div \frac{5}{4}$ )T2

= ( $\frac{1}{2} \times \frac{4}{5}$ )25 = 10

Hence p : q : r = 12: 15 : 10

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