Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 11
There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first ?

A
Cyclist
B
Boat Sailor
C
Cannot be determined
D
None of these
Correct Answer: Option A

Clearly, the cyclist moves both ways at a speed of 12 km/hr.

So, average speed of the cyclist = 12 km/hr.

The boat sailor moves downstream @ (10 + 4)

i.e 14 km/hr and upstream @ (10 - 4) i.e, 6 km/hr.

So, average speed of the boat sailor :

= 2 x 14 x 6/14 +6 km/hr.

= 42/5 km/hr = 8.4 km/hr.

Since the average speed of the cyclist is greater, he will return to A first.

Question 12
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10mph, the speed of the stream is :

A
2 mph
B
2.5 mph
C
3 mph
D
4 mph
Correct Answer: Option A

Let the speed of the stream x mph. Then,

Speed downstream = (10 + x) mph,

Speed upstream = (10 - x) mph.

36 - 36 = 90
(10 - x) (10 + x) 60

72x x 60 = 90 (100 - x2)

x2 + 48x - 100 = 0

(x+ 50)(x - 2) = 0

x = 2 mph.

Question 13
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

A
12 kmph
B
13 kmph
C
14 kmph
D
15 kmph
E
None of these
Correct Answer: Option D

Let the speed of the boat in still water be x kmph. Then,

Speed downstream = (x + 3) kmph,

Speed upstream = (x - 3) kmph.

(x + 3) x 1 = (x - 3) x 3
2

2x + 6 = 3x - 9

x = 15 kmph.

Question 14
A man can row at 5 kmph in still water is 15 km/hr and the rate of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place ?

A
2.4 km
B
2.5 km
C
3 km
D
3.6 km
Correct Answer: Option A

Speed downstream = (5 + 1) kmph = 6 kmph.

Speed upstream = (5 - 1) kmph = 4 kmph.

Let the required distance be x km.

Then, x + x = 1
6 4

2x + 3x = 12

5x = 12

x = 2.4 km.

Question 15
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
A
2 hours
B
3 hours
C
4 hours
D
5 hours
Correct Answer: Option C

Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream = 68 hrs
17

= 4 hrs.

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