Given that \(W : X = 5 : 6,\ X : Y = 3 : 7,\ \text{and}\ Y : Z = 8 : 9\), find the compound ratio \(W : X : Y : Z\).
20 : 24 : 56 : 63
Step 1 – Make X consistent in W:X and X:Y.
\(W : X = 5 : 6\) and \(X : Y = 3 : 7\). Scale the second to make X = 6: \(X : Y = 6 : 14\).
So \(W : X : Y = 5 : 6 : 14\).
Step 2 – Make Y consistent in W:X:Y and Y:Z.
Y is 14 in the first chain and 8 in the second. LCM(14, 8) = 56.
Scale \(W : X : Y = 5 : 6 : 14\) by 4 → \(20 : 24 : 56\).
Scale \(Y : Z = 8 : 9\) by 7 → \(56 : 63\).
Step 3 – Combine.
\(W : X : Y : Z = 20 : 24 : 56 : 63\).
Similar Questions
If P : Q = 6 : 11, Q : R = 5 : 4, and R : S = 9 : 7, find P : Q : R : S.
Important Questions from Compound Ratios
The train fare, bus fare and air fare between 2 places are in the ratio 5 : 8 : 12, the number of passenger travelled by them is in the ratio 3 : 4 : 5 and the total fare collected on a particular day for these modes of transportation for a single trip is Rs. 1,07,000. Find the fare collected from the air passengers.
The compounded ratio of (1 ∶ 3), (6 ∶ 5) and (7 ∶10) is:
Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is A’s share?
Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is B’s share?
Two numbers are in the ratio 3 : 5. If 4 is subtracted from each of these two numbers, the new numbers then are in the ratio 4 : 7. Find the smaller of the two original numbers.
