Question

Two sisters Neha and Monica walk to school from the house. Neha takes 40 minutes while Monica takes 30 minutes. One day Neha started 5 minutes earlier than Monica. In how many minutes would Monica overtake Neha?

• A. 5
• B. 15
• C. 20
• D. 25

Answer 1

The Correct Option is B

To solve this problem, we need to find the time it will take for Monica to overtake Neha, given their walking times to school. 

1. First, understand their walking speeds. Both sisters walk the same distance from home to school.
   • Let the distance to school be \(D\).
   • Neha takes 40 minutes to walk this distance: her speed \(= \frac{D}{40}\) minutes per unit distance.
   • Monica takes 30 minutes: her speed \(= \frac{D}{30}\) minutes per unit distance.
2. Since Neha starts 5 minutes earlier, she has a 5-minute head start. In that time, the distance she covers is:
   • Distance covered by Neha \(= \left(\frac{D}{40}\right) \times 5 = \frac{D}{8}\)
3. Now, Monica starts walking. Monica needs to cover this additional distance \(\frac{D}{8}\) to overtake Neha.
4. The relative speed of Monica with respect to Neha is:
   • Relative speed \(= \frac{D}{30} - \frac{D}{40}\)
   • Simplifying, we get: \(\frac{D}{30} = \frac{4D}{120}\) and \(\frac{D}{40} = \frac{3D}{120}\)
   • Thus, relative speed \(= \frac{4D}{120} - \frac{3D}{120} = \frac{D}{120}\)
5. The time taken by Monica to overtake Neha can be calculated as:
   • \(\text{Time} = \frac{\frac{D}{8}}{\frac{D}{120}} = \frac{D}{8} \times \frac{120}{D} = 15 \text{ minutes}\)

Monica will overtake Neha in 15 minutes after she starts walking.