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 journeys and brought a certain quantity of water. In how many journeys would 12 large, 14 medium and 21 small ships bring the same quantity ?

Options

A. 32
B. 25
C. 29
D. 49

Answer

C

Explanation

Let the quantity of water carried by large, medium and small ships be L, M and S respectively.
According to the question
`4L = 7S " " .....(i)`
`3M = 2L+S " " ...(ii)`
From (i), we get `L = 7/4 S`.
Putting L= Sin (ii), we get
`3M = 2 xx (7/4 S) + S =7/2 S + S = (9S)/2`
or `M = 3/2 S`
So `15L + 7M + 14S = 7/4 xx 15S + 3/2 x 7S + 14S`
`= (105)/4 S + 21/2 S + 14S`
`= (105 S + 42 S + 56 S)/(4) = 203/4 S`
`therefore` Number of Journeys by `203/4 S = 36` [Given]
So, Total quantity of water carried = `(203S)/4 xx 36 = 1827S`
Now, `12L + 14M + 21S = 7/4 xx 12S + 3/2 xx 14S + 21S`
`= 21 S + 21S + 21S = 63S`
Therefore, Required Number of Journeys by 63S
`= ("Total quantity of water carried")/(63 S) = (1827 S)/(63 S) = 29`