Dot Cabs has 8 Swift Dzire cars, 6 Scorpios, 7 Innovas and some small cars. If the number of Swift Dzire cars is one-fourth of the total fleet, how many small cars does the company have?

Introduction / Context:
This question is a simple application of ratios and fractions in a real world setting. The total fleet of cars in a cab company includes different types of vehicles, and we know that one particular type (Swift Dzire) constitutes one-fourth of the entire fleet. By treating the total as an unknown and using the given counts of specific vehicles, we can determine how many small cars must be present so that Swift Dzire cars make up exactly one-fourth of the total fleet.

Given Data / Assumptions:

• Number of Swift Dzire cars = 8.
• Number of Scorpios = 6.
• Number of Innovas = 7.
• Number of small cars = S (unknown).
• The number of Swift Dzire cars is one-fourth of the total number of cars in the fleet.
• Total fleet size = Swift Dzire + Scorpios + Innovas + small cars.

Concept / Approach:
Let the total number of cars be T. Then T = 8 + 6 + 7 + S. The condition “Swift Dzire makes one-fourth of the total fleet” means 8 = (1 / 4) * T. We can use this relation to express T and then find S. This is a straightforward algebraic problem involving solving a linear equation in one variable.

Step-by-Step Solution:
Step 1: Let the total number of cars be T. Step 2: We know that T = 8 (Swift Dzire) + 6 (Scorpios) + 7 (Innovas) + S (small cars). So T = 21 + S. Step 3: The number of Swift Dzire cars is one-fourth of the total fleet. So 8 = (1 / 4) * T. Step 4: Multiply both sides by 4: T = 4 * 8 = 32. Step 5: Now use T = 21 + S: 21 + S = 32. Step 6: Solve for S: S = 32 - 21 = 11. Step 7: Hence the company has 11 small cars.

Verification / Alternative check:
We can verify by recomputing the total fleet with S = 11. Total = 8 + 6 + 7 + 11 = 32 cars. One-fourth of 32 is 32 / 4 = 8, which matches the given number of Swift Dzire cars. Therefore, our solution is consistent and correct.

Why Other Options Are Wrong:
If S were 9, total would be 30, and one-fourth of 30 is 7.5, not 8. If S were 10, total would be 31, and one-fourth of 31 is not an integer and certainly not 8. If S were 12, total would be 33, and one-fourth of 33 is 8.25. Only S = 11 produces a total where Swift Dzire cars are exactly one-fourth of the fleet.

Common Pitfalls:
Learners sometimes misinterpret “one-fourth of the total fleet” as “Swift Dzire is one-fourth more than some other category” or confuse which quantity is supposed to be a fraction of which. Another mistake is to forget to include all car types in the total. It is important to define variables clearly, write down the total explicitly and translate the fractional relationship into an equation before solving.

Final Answer:
Dot Cabs has 11 small cars in its fleet.