Aptitude Solved Problems Find the rate of the stream?

Aptitude Solved Problems
Find the rate of the stream?

1. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?

Answer: 9 seconds.

Explanation:

Speed of the train relative to man = ( 68 - 8 ) km/hr
= 60 km/hr
To convert km/hr to m/sec
= ( 60 * ( 5 / 18 ) ) m/sec
= ( 50 / 3 ) m/sec
Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50 / 3 ) m/sec
= ( 150 * ( 3 / 50 ) ) sec
= 3 * 3
= 9 sec

∴ In 9 sec it will pass the man.


2. The average of a non - zero number & its square is 7 times the number . Then find the number?

Answer: 13.

Explanation:

Let the number be x.
( x + x2 ) / 2 = 7x
x + x2 = 7x * 2
x + x2 = 14x
x + x2 - 14x = 0
x2 + x - 14x = 0
x2 - 13x = 0
x * ( x - 13 ) = 0
x = 0 ( or ) x - 13 = 0
Given that the number is non zero so
x = 13

∴ The number is 13.


3. Three partners P, Q and R invest a total sum of 240000. At the end of the year P get 15000 rupee, Q get 20000 and R get 25000 rupees as profit. How much amount is invested by P and R together?

Answer: Rs. 16000.

Explanation:

Ratio in which they get profit = 3 : 4 : 5
Total ratio = ( 3 + 4 + 5 )
= 12
So total amount invested by P and R = ( 8 / 12 ) * 24000
= ( 8 * 2000 )
= 16000

∴ P and R together invested Rs. 16000.


4. A man can row 15 km/hr in still water. It takes him twice as long to row upstream as to row downstream. Find the rate of stream?

Answer: 5 km/hr.

Explanation:

Let man′s rate in upstream be x km/hr, then his rate in downstream is be 2x km/hr
Rate in still water = ( 1 / 2 ) ( Rate downstream + Rate upstream )
= ( 1 / 2 ) ( 2x + x )
= ( 3x / 2 ) km/hr
( 3x / 2 ) = 15
x = ( 15 * 2 ) / 3
x = 10 km/hr
So rate downstream= 2x
= 20 km/hr
Rate of stream = ( 1 / 2 ) ( Rate downstream - Rate upstream )
= ( 1 / 2 ) ( 20 - 10 )
= 5 km/hr

∴ The rate of stream is 5 km/hr.







Sharpe

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