Question 55

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 ?

Solution

Let the large ships be l, medium be m and small be s.

From the information given , we get

4l = 7s

3m = 2l + 1s

6m = 4l + 2s, so 6m = 9s, so 2m = 3s, m = 3s/2 = 6l/7

Total quantity of water in 36 journeys:

t = 36*[15l + 7m + 14s] = 36*[15l+6l+8l] = 36*29l

t = x [12l+14m+21s], x = number of journeys

36*29l = x[12l + 12l + 12l] = 36l*x

x = 29 journeys

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