Question

If A and B are in the ratio 2:3, B and C are in the ratio 1:2 and C and D are in the ratio 1:3, compare the ratios A:D and A:C.

Answer 1

GOAL: To write all parameters in terms of any one of the parameters. Here, all parameters are being written in terms of B.

Let A:B = 2:3
=> A/B = 2/3
=>A = 2B/3 --------------- (i)

B:C = 1:2
=> B/C = 1/2
=> C = 2B ----------------- (ii)

C:D = 1:3
=> D = 3C
=> D = 3 x 2B = 6B (from (ii)) -------- (iii)

Now from (i) and (iii),
A:D = 2B/3 : 6B = 1:9
and from (i) and (ii),
A:C = 2B/3 : 2B = 1:3

Now we have to compare the ratios 1:9 and 1:3.
Cross multiplying,
3<9.
Therefore 1:9 < 1:3
=>A:D < A:C