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If p : q = 23 : 56 and q : r = \(\...

If p : q = 23 : 56 and q : r = 34 : 12, find p : q : r

A.

12 : 15 : 10

B.

12 : 15 : 16

C.

10 : 15 : 24

D.

9 : 10 : 15

Correct answer is A

If p : q = 23 : 56, then the sum S1 of ratio = 23 + 56 = 96

If q : r = 34 : 12, then the sum S2 of ratio = 34 + 12 = 54

Let p + q = T1, then

q = (56÷96)T1 = (56×69)T1 = 59T1

Again, let q + r = T2, then

q = (34÷54)T2 = (34×45)T2 = 35T2

Using q = q

59T1 = 35T2

5 x 5T1 = 9 x 3T2

T1T2 = 9×35x5 = 2725

Giving that, T1 = 27 and T2 = 25

P = (23÷S1)T1 = (23÷96)T1

= (23×69)27 = 12

q = (56÷S1)T1 = (56÷96)T1

= (56×69)27 = 15

and r = (12÷S2)T2 = (12÷54)T2

= (12×45)25 = 10

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