1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current will be 10 km/hr.
2. The speed of a boat in still water is 22 km/hr. and the rate of current flow is 3 km/hr. The distance travelled in downstream direction in 12 minutes will be 5 km.
Select the answer using the code given below:
To determine the correctness of the statements given in the question, let's analyze each one by applying relevant concepts.
- Statement 1: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current will be 10 km/hr.
- Let's denote: \(S_m\) = Speed of the man in still water (unknown), \(S_c\) = Speed of the current = 2.5 km/hr.
- The man's speed with the current is given by \(S_m + S_c = 15\, \text{km/hr}\).
- Hence, \(S_m = 15 - 2.5 = 12.5\, \text{km/hr}\).
- The man's speed against the current would be \(S_m - S_c = 12.5 - 2.5 = 10\, \text{km/hr}\). Thus, statement 1 is correct.
- Statement 2: The speed of a boat in still water is 22 km/hr, and the rate of current flow is 3 km/hr. The distance travelled in the downstream direction in 12 minutes will be 5 km.
- The speed of the boat in downstream is \(S_b + S_c = 22 + 3 = 25\, \text{km/hr}\).
- Time given is 12 minutes, which is \(\frac{12}{60} = \frac{1}{5}\) hours.
- Distance travelled downstream = Speed × Time = \(25 \times \frac{1}{5} = 5\, \text{km}\). Thus, statement 2 is also correct.
Based on the analysis of both statements, the correct answer is Both 1 and 2.
Important Questions from Partial Speed
Amit travelled a distance of 50 km in 9 hours. He travelled partly on foot at 5 km/h and partly by bicycle at 10 km/h. The distance travelled on the bicycle is:
Walking at 3/5 of his usual speed, a person reaches his office 20 minute later than the usual time. His usual time in minutes is:
Walking at 7/9 of his usual speed, a person reaches his office 10 minutes later than the usual time. His usual time in minutes is:
A man travelled a distance of 42 km in 5 hours. He travelled partly on foot at the rate of 6 km/h and partly on bicycle at the rate of 10 km/h. The distance travelled on foot is:
A train takes \(2\frac{1}{2}\) hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed?
