JKSSB Mental Ability Paper

Explanation

1. Identify the Speeds

• Speed of the man in still water ($u$): $6\text{ km/hr}$

• Speed of the current ($v$): $2\text{ km/hr}$

• Speed downstream ($u + v$): $6 + 2 = 8\text{ km/hr}$

• Speed upstream ($u - v$): $6 - 2 = 4\text{ km/hr}$

2. Set up the Equation

Let the distance to the place be $d$. The total time taken for the round trip is the sum of the time taken to go downstream and the time taken to return upstream.

$$\text{Total Time} = \text{Time Downstream} + \text{Time Upstream}$$

Given that the total time is $3$ hours:

$$3 = \frac{d}{8} + \frac{d}{4}$$

3. Solve for $d$

To solve the equation, find a common denominator (which is $8$):

$$3 = \frac{d}{8} + \frac{2d}{8}$$

$$3 = \frac{3d}{8}$$

Multiply both sides by $8$:

$$24 = 3d$$

$$d = \frac{24}{3}$$

$$d = 8$$

The distance to the place is 8 km.

Explanation

Time of stop = (Difference in speed / Faster speed) * 60 = (9 / 54) * 60 = 1/6 * 60 = 10 minutes.

Explanation

Average speed = (2 * S1 * S2) / (S1 + S2) = (2 * 40 * 10) / (40 + 10) = 800 / 50 = 16 km/hr.

Explanation

The speed of the boat in still water is approximately 7.45 km/h.

Explanation

Relative speed = 2 km/hr. Time to catch = 0.2 km / 2 km/hr = 0.1 hour. Distance run by thief = 10 km/hr * 0.1 hr = 1 km = 1000 m.

Explanation

Speed ratio = 3:4, so Time ratio = 4:3. Difference in time = 1 unit. Given 1 unit = 20 mins. Usual time = 3 units = 60 minutes.

Explanation

Relative speed = 60 + 90 = 150 km/hr. Total distance = 1.1 + 0.9 = 2 km. Time = 2 / 150 hours = (2 / 150) * 3600 seconds = 48 seconds.

Explanation

Average Speed = 3 / (1/3 + 1/4 + 1/5) = 3 / (20+15+12 / 60) = 180 / 47 = 3.83 km/hr.

Explanation

Speed = Distance / Time = 150 / 15 = 10 m/s. To convert to km/hr, multiply by 18/5. 10 * (18/5) = 36 km/hr.

Explanation

Speed = 450 / 9 = 50 km/hr. To convert to m/s, multiply by 5/18. 50 * (5/18) = 250 / 18 = 13.88 m/s.