The following ratios are given: \(a : b = 2 : 3\) \(b : c = 4 : 5\) \(c : d = 3 : 2\) \(d : e = 5 : 4\) What is the value of the ratio a : e?
1 : 1
The combined ratio \(a:e\) is obtained by multiplying all the given ratios together:
\(\frac{a}{e} = \frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} \times \frac{d}{e} = \frac{2}{3} \times \frac{4}{5} \times \frac{3}{2} \times \frac{5}{4}\).
Simplifying, \(\frac{2 \times 4 \times 3 \times 5}{3 \times 5 \times 2 \times 4} = 1\).
So \(a:e = 1:1\).
Hence, the ratio a : e is 1 : 1.
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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.
