Vases-Flowers

Puzzle Level :- Easy

PUZZLE

Mrs. John has some flowers and vases to decorate hall.

• If she keeps one flower in each vase, one flower will remain
• If she keeps two flowers in each vase, one vase will be empty

How many vases and flowers she has.

ANSWER

3-Vases

4-Flowers

SOLUTION

Let's assume  she has X vases and Y flowers.

so from first statement "If she keeps one flower in each vase, one flower will remain"
we can make equation

X*1 +1= Y       (i,e   each vase * one flower + extra flower = total flowers )

and  from second statement "If she keeps two flowers in each vase, one vase will be empty"

(X-1)*2 = Y    (i,e   (total vases - one extra vase) *   two flowers in each vase  = total flowers )

So equations are
1)  X+1 =Y
2)  (X-1)*2 =Y

replace statement 1 in 2

(X-1)*2 =X+1  ==>    2X-2 = X+1   ==>  2X=X+3

 ==>  2X-X = 3    ==>   X=3

So No of Vases are 3

If we substitute it in first statement

X+1=Y  ==>   3+1 = Y  ==>  Y=4

So no of flowers are 4

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