Vijay can cover a distance *D* with speed *S* in time *T*. He can cover the same distance with speed *(S + 10)* in time *(T - 2)*. He can cover the same distance *D* with speed *(S - 15)* in time *(T + 6)*. Based on this data, which of the following can be found?

(i) Time to cover 200 km with speed *(S + 10)*

(ii) Distance covered in *(T + 6)* time with speed *(S + 10)*

(iii) Speed by which a tunnel can be crossed in *\frac{T}{2}* hour

(iv) Ratio between time to cover distance *D* with speed *S* to time to cover distance *(D - 5)* with speed *(S + 10)*

Question

Vijay can cover a distance *D* with speed *S* in time *T*. He can cover the same distance with speed *(S + 10)* in time *(T - 2)*. He can cover the same distance *D* with speed *(S - 15)* in time *(T + 6)*. Based on this data, which of the following can be found?

(i) Time to cover 200 km with speed *(S + 10)*

(ii) Distance covered in *(T + 6)* time with speed *(S + 10)*

(iii) Speed by which a tunnel can be crossed in *\frac{T}{2}* hour

(iv) Ratio between time to cover distance *D* with speed *S* to time to cover distance *(D - 5)* with speed *(S + 10)*

Accepted Answer

**Solution:**

1. Given:
   - Distance = *D*
   - Speed = *S*
   - Time = *T*

2. From the problem, we have three equations:
   $$ S = \frac{D}{T} \quad 	ext{...(i)} $$
   $$ S + 10 = \frac{D}{T - 2} \quad 	ext{...(ii)} $$
   $$ S - 15 = \frac{D}{T + 6} \quad 	ext{...(iii)} $$

3. Solving these simultaneously (as given):
   - *D* = 400 km
   - *S* = 40 km/h
   - *T* = 10 hours

4. Now, analyze each statement:

(i) Time to cover 200 km with speed *(S + 10)*:
   - Speed = 40 + 10 = 50 km/h
   - Time = Distance / Speed = 200 / 50 = 4 hours
   - This can be found.

(ii) Distance covered in *(T + 6)* time with speed *(S + 10)*:
   - Time = 10 + 6 = 16 hours
   - Speed = 50 km/h
   - Distance = Speed × Time = 50 × 16 = 800 km
   - This can be found.

(iii) Speed by which a tunnel can be crossed in *\frac{T}{2}* hour:
   - The length of the tunnel is not given.
   - Without tunnel length, speed cannot be determined.
   - This cannot be found.

(iv) Ratio between time to cover distance *D* with speed *S* to time to cover distance *(D - 5)* with speed *(S + 10)*:
   - Time1 = D / S = 400 / 40 = 10 hours
   - Time2 = (D - 5) / (S + 10) = (400 - 5) / 50 = 395 / 50 = 7.9 hours
   - Ratio = 10 : 7.9
   - This can be found.

**Answer:** only (i), (ii) and (iv) (Option e)

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