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Q.

Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships.

3 medium ships carry the same amount of water as 2 large ships and 1 small ship. 

15 large, 7 medium and 14 small ships, each made 36 journey and brought a certain quantity of water.

In how many journeys would 12 large, 14 medium and 21 small ships bring the same quantity?

 A.

32

 B.

29

 C.

49

 D.

25

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Solution:
Option(B) is correct

Let, $L=$ large ships, $M=$ medium ships, $S=$ small ships

Now from the question,

$4L=7S$

$\Rightarrow \dfrac{L}{S}=\dfrac{7}{4}$

$\Rightarrow L= 7x; S= 4x$

$3M= 2L+S$

$\Rightarrow M= \dfrac{2 \times 7x+4x}{3}$

$\Rightarrow M= 6x$

Thus, ratio of large, medium and small $=7:6:4$

So, numbers of journeys:

\(=\dfrac{(15\times7+7\times6+14\times4)36}{12\times 7+14\times 6+21\times 4}\)

\(=\dfrac{7308}{252}\)

\(=29\)

Note: Thank you Ruchi for the explaination to calculate the ratio of large, medium and small ships. Updated the solution accordingly.

Thank you Mrigendra Pratap Singh for pointing out a mistake, updated the question accordingly.


(9) Comment(s)


Poonam Pipaliya
 ()

Sir,

In first line there is 4 large ships carry so you multiplied $L$ by 4 but in second line there is 3 medium ships carry the same amount as..........

So why you don't multiply $M$ by 3?

I don't get it. Please elaborate.


Deepak
 ()

You are correct Poonam, there was a typo in the solution. Answer has been updated.


Mrigendra Pratap Singh
 ()

Explanation is good, though there is some mistake in the question.

Correction: - the 3 medium ships carry the same amount of water as "2" (it was missing) large ship and 1 small ship".


Deepak
 ()

Thank you for suggesting a correction. Updated the question accordingly.


Kaushal
 ()

3 medium ships carry the same amount of water as large ship and 1 small ship..

There is only one large ship then why are you taking two large ship please let me know about it.

Am I right or wrong?



Ruchi
 ()

$L=$ large ships

$M=$ medium ships

$S=$ small ships

no. of ships:

$4L=7s$

$\Rightarrow \dfrac{L}{S}=\dfrac{7}{4}$

$\Rightarrow L= 7x; S= 4x$

$M= 2L+S$

$= \dfrac{2 \times 7x+4x}{3}= 6x$


Deepak
 ()

Thank you for bringing this nice explanation. Updated the solution taking inputs from your comment.


Jas Sahib
 ()

The question is wrong , its two large ships and 1 small ship , thus making our ratio for the medium ship as,

$\dfrac{7 \times 2x+4x}{3}=6x$



Jayanth
 ()

Dear All,

Not clear about the ratio, $7:6:4$.

any logic for this ratio?