A hall of length 24 cm and breadth 20 m is to be paved with equal square tiles. What will be the size of the largest tile so that the tiles exactly fi t and also find the number of tiles required.
Size of the largest possible square tile
= H.C.F. (l, b)
= H.C.F. (24, 20) = 4 m
Number of tiles required
= l x b / H.C.F. (24, 20)
= 24 x 20 / 4 = 120 tiles.
Ahmed is thrice as good a workman as Balkar and takes 22 days less to complete a piece of work than Balkar takes. Find out time in which Balkar alone can complete the work.
The word NANAKMATTA has 10 letters in all. The letter ‘A’ occurs 4 times, the letter ‘N’ occurs 2, letter ‘T’ occurs 2 times and the remaining two letters K & M each occur once.
∴ The require number of permutations
= 10! /4!2!2!1!1!
= 10! /4!2!2!
= (10*9*8*7*6*5*4!)/4!2*2
= (10*9*4*7*3*5)
= 37800