Question

In covering a distance of 72 km, Amit takes 5 hours more than Vinay. If Amit doubles his speed, then he would take 7 hour less than Vinay. Amit's speed is:

• A. 1 km/h
• B. 3 km/h
• C. 5 km/h
• D. 6 km/h

Answer 1

Answer:

B. 3 km/h

Amit's speed is 3 km/h.

1. Formulate the Equations:
Let Amit's speed be $x$ km/h and Vinay's speed be $y$ km/h. Using the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$:

• Case 1: Amit takes 5 hours more than Vinay to cover 72 km.
  $\frac{72}{x} - \frac{72}{y} = 5 \quad \text{--- (Equation 1)}$

• Case 2: If Amit doubles his speed ($2x$), he takes 7 hours less than Vinay.
  $\frac{72}{y} - \frac{72}{2x} = 7 \quad \rightarrow \quad \frac{72}{y} - \frac{36}{x} = 7 \quad \text{--- (Equation 2)}$

2. Solve for $x$ (Amit's Speed):
Add Equation 1 and Equation 2 together to eliminate the $\frac{72}{y}$ term:
$\left(\frac{72}{x} - \frac{72}{y}\right) + \left(\frac{72}{y} - \frac{36}{x}\right) = 5 + 7$
$\frac{72}{x} - \frac{36}{x} = 12$
$\frac{36}{x} = 12$
$x = \frac{36}{12} = \mathbf{3\text{ km/h}}$