The train fare and bus fare between two stations is in the ratio 3 : 4. If the train fare increases by 20% and bus fare increases by 30%, then what is the ratio between revised train fare and revised bus fare?Options9 : 1332 : 4319 : 2117 : 12
Question
The train fare and bus fare between two stations is in the ratio 3 : 4. If the train fare increases by 20% and bus fare increases by 30%, then what is the ratio between revised train fare and revised bus fare?Options9 : 1332 : 4319 : 2117 : 12
Solution
Let's solve this step by step:
Step 1: Let's assume the initial train fare is 3x and the initial bus fare is 4x.
Step 2: The train fare increases by 20%. So, the new train fare is 3x + 20% of 3x = 3x + 0.6x = 3.6x.
Step 3: The bus fare increases by 30%. So, the new bus fare is 4x + 30% of 4x = 4x + 1.2x = 5.2x.
Step 4: The new ratio of the train fare to the bus fare is 3.6x : 5.2x.
Step 5: To simplify this ratio, we can divide both sides by the common factor, which is 0.4x.
So, the simplified ratio is (3.6x/0.4x) : (5.2x/0.4x) = 9 : 13.
Therefore, the ratio between the revised train fare and the revised bus fare is 9 : 13.
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