Question

A gardener has to plant trees in rows containing equal number of trees. if he plants in rows of 6, 8, 10 or 12, then five trees are left unplanted. but if he plants in rows of 13 trees each, then no tree is left. what is the number of trees that the gardener plants?

Answer 1

There are nomire trees left to plant

Answer 2

Solution :-

L.C.M. of 6, 8, 10 and 12

6 = 2*3

8 = 2*2*2

10 = 2*5

12 = 2*2*3

L.C.M. of 6, 8, 10 and 12 = 2*2*2*3*5 = 120

When equal number of trees are planted in rows of 6, 8, 10 or 12, five trees are left unplanted.

Hence, number of trees will be (120x + 5), which must be divided by 13 as per the given condition in the question.

By hit and trial method =

(120x + 5)/13 will be satisfied for x = 7

(120*7) + 5

So, total number of trees = 840 + 5 = 845

845 is exactly divisible by 13.

Answer.