7
Q:

# Mr. Karthik drives to work at an average speed of 48 km/hr. Time taken to cover the first 60% of the distance is 20 minutes more than the time taken to cover the remaining distance. Then how far is his office ?

 A) 40 km B) 50 km C) 70 km D) 80 km

Explanation:

Let the total distance be 'x' km.
Time taken to cover remaining 40% of x distance is   $\inline \fn_jvn t1 = \frac{40 \times x}{100\times 48}$
But given time taken to cover first 60% of x distance is   $\inline \fn_jvn t2 = t1 + \frac{20}{60}hrs$
$\fn_jvn&space;\Rightarrow$ $\inline \fn_jvn t2 = \frac{60 \times x}{100 \times 48}$

$\inline \fn_jvn \small \therefore \frac{60\times x}{100 \times 48}=\frac{40\times x}{100\times 48}+\frac{20}{60}$ $\fn_jvn&space;\small&space;\Rightarrow$ x=80 km.

Q:

A motorboat can go 10 miles downstream on a river in 20 min. It takes 30 min for this boat to go back at the same 10 miles. Find the speed of the current ?

 A) 8 m/h B) 5 m/h C) 7 m/h D) 6 m/h

Explanation:

As the distance travelled is constant, the time taken is inversely proportional to speed.

Let 'u' be the speed of the current and 'v' be the speed of the boat.

Speed of the boat downstream = v + u & upstream = v - u

=> v+u/v-u = 30/20 => v/u = 5 => v = 5u

=> v + u = 6u = 10/20/60 miles/hr

=> 6u = 30 m/h

=> u = 5 m/h

8 129
Q:

If a girl cycles at 10 kmph, then she arrives at a certain place at 1 p.m. If she cycles at 15 kmph, she will arrive at the same place at 11 a.m. At what speed must she cycle to get there at noon?

 A) 14 kmph B) 13 kmph C) 12 kmph D) 11 kmph

Explanation:

The distance is constant in this case.

Let the time taken for travel with a speed of 10 kmph be 't'.

Now the speed of 15 kmph is 3/2 times the speed of 10 kmph.

Therefore, time taken with the speed of 15 kmph will be 2t/3 (speed is inversely proportional to time)

Extra time taken = t - 2t/3 = t/3

=> 1pm - 11am = 2hrs

=> t/3 = 2h

=> t = 6 hrs.

Now, Distance = speed x time = 10 x 6 = 60 kms

Time he takes to reach at noon = 6 - 1 = 5 hrs

Now, Speed = 60/5 = 12 kmph.

9 118
Q:

A boat whose speed in still water is 9 kmph, goes 12 km downstream and comes back in 3 hrs. Find the speed of the stream?

 A) 1 kmph B) 3 kmph C) 5 kmph D) 4 kmph

Explanation:

Let the speed of the stream = x kmph

From the given data,

$\inline \fn_jvn \frac{12}{9+x}+\frac{12}{9-x} = 3 hrs$

$\inline \fn_jvn 3x^{2} = 27$

=> x = 3 kmph

Therefore, the speed of the stream = 3 kmph

9 117
Q:

In a daily morning walk three persons step off together. their steps measure 75 cm, 80 cm and 85 cm respectively. What is the minimum distance each should walk so that thay can cover the distance in complete steps  ?

 A) 222 m 44 cm B) 204 m C) 201 m 21 cm D) 208 m

Explanation:

To find the minimum distance, we have to get the LCM of 75, 80, 85

Now, LCM of 75, 80, 85 = 5 x 15 x 16 x 17 = 20400

Hence, the minimum distance each should walk so that thay can cover the distance in complete steps = 20400 cms = 20400/100 = 204 mts.

5 79
Q:

Three friends Rudra, Siva and Anvesh start to run around a circular stadium. They complete a revolution in 24, 36 and 30 seconds respectively. After how many minutes will they meet at the starting point ?

 A) 60 B) 120 C) 360 D) 6