In a map, 1.5 cm represents 46.8 km. How much distance will be represented by 3.5 cm on the map?

1. 96.4 km
2. 98.5 km
3. 109.2 km
4. 113.6 km

Given:

Distance for 1.5 cm = 46.8 km

Distance for 1 cm = $\dfrac{46.8}{1.5} \text{ km} \quad \text{[Less cm, Less distance]}$

Distance for 3.5 cm = $\Big(\dfrac{46.8}{1.5} \times 3.5\Big) \text{ km} \quad \text{[More cm, More distance]}$

Multiply by 10 to remove decimals:

= $\Big(\dfrac{46.8 \times 10}{1.5 \times 10} \times 3.5\Big) \text{ km} = \Big(\dfrac{468}{15} \times 3.5\Big)$ km

= 31.2 x 3.5 km $\quad$ [Dividing 468 and 15 by 15]

= 109.2 km

Hence, option 3 is the correct option.