Time, Speed & Distance
Aptitude

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Q.

A ship 77 km from the shore, springs a leak which admits to 9/4 tonnes of water in 11/2 minutes. 92 tonnes of water would sink it. But the pumps can throw out 12 tonnes of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.

 A.

10.5 km/hr

 B.

11 km/hr

 C.

10 km/hr

 D.

12.5 km/hr

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Solution:
Option(A) is correct

Given leak admits \(\dfrac{9}{4}\) tonnes of water in \(\dfrac{11}{2}\)min.

Leak admits one tank of water 

 

\(=\dfrac{11}{2}\times \dfrac{4}{9}\)

\(=\dfrac{22}{9}\text{ min}\)
Leak admits \(\dfrac{9}{22}\)tonne of water in one min

Now, pump throws 12 tonne of water in 60 min.

Pump throws 1 tonne of water in 5 min.

In 1 minutes it throws \(\dfrac{1}{5}\)  tonne of water.

 

Water accumulated in the ship in 1 min: 
\(=\dfrac{9}{22}-\dfrac{1}{5}\)

\(=\dfrac{23}{110} \) tonnes or 92 tonnes

Water, sufficient to get the ship sunk can be accumulated in: 

\(=\dfrac{92}{23/11}\text{ min}\)

\(=440\text{ min}\)

\(=\dfrac{22}{3}\text{ min}\)

Rate of sailing in order that the ship may just reach the shore: 

\(=\dfrac{7/22}{22/3}\)

$⇒$ 10.5 km/hr

Edit: A typo in the question has been modified after it was pointed by Krish.


(2) Comment(s)


Nimish Gupta
 ()

9/4 tonnes in 11/2 minutes so in 1 min 2.25/5.5 tonnes water will come in.

in 60 min 2.25*60/5.5 i.e 24.54 and the pump empty 12 tonnes every hour so in 1 hour 12 tonne water will be left on the ship. In 92/12 minutes ship will sink i.e 7.66 so by looking at the option we can find the answer i.e 10.5kmph( 77/10.5 = 7.3)



Krish
 ()

In question it says 9/2 tones is leaking but in solution its says 9/4 tones leaking in 11/2 mins..!!!!!???