Question

In an express train, the numbers of passengers travelling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio $1:2:3$, and the fares of these classes are in the ratio $5:4:2$. If the total income from the train is ₹ 54000, find the income from the A.C. Sleeper Class.

• A. ₹ 8000
• B. ₹ 12000
• C. ₹ 10000
• D. None of these

Hint:

When both numbers and fares are in ratios, income share equals the product of the corresponding ratios. Sum the parts and allocate the total accordingly.

Answer 1

The Correct Option is D

Step 1: Convert to income ratio.
Numbers ratio $=1:2:3$. Fares ratio $=5:4:2$.
$\Rightarrow Income \,\, ratio =(1\cdot 5):(2\cdot 4):(3\cdot 2)=5:8:6. $

Step 2: Split total by parts.
Total income $=₹ 54000$ is split in $5+8+6=19$ parts.
$\Rightarrow A.C. income =\dfrac{5}{19}\times ₹ 54000=₹ 14210.526\dots $

Step 3: Match with options.
$₹ 14210.526\dots$ does not equal ₹ 8000, ₹ 10000, or ₹ 12000.
$\Rightarrow\ \boxed{\text{None of these}}.$