There are 3 shrines, each with a magical pond in the front. If anyone dips flowers into these magical ponds Class 8

There are 3 shrines, each with a magical pond in the front. If anyone dips flowers into these magical ponds Class 8

Question 1.

There are 3 shrines, each with a magical pond in the front. If anyone dips flowers into these magical ponds, the number of flowers doubles. A person has some flowers. He dips them all in the first pond and then places some flowers in shrine 1. Next, he dips the remaining flowers in the second pond and places some flowers in shrine 2. Finally, he dips the remaining flowers in the third pond and then places them all in shrine 3. If he placed an equal number of flowers in each shrine, how many flowers did he start with? How many flowers did he place in each shrine? Class 8

Solution:

Let in the beginning, he was having x flowers.

After the first dip, number of flowers = 2x.

Let he places y flowers in the shrine 1, remaining flowers = 2x - y.

So, after a dip in the second pond,

number of flowers = 2 (2x - y) = 4x - 2y.

After placing y flowers in the shrine 2,

remaining flowers = 4x - 2y - y.

= 4x - 3y.

After a dip in the third pond,

number of flowers = 2 (4x - 3y) = 8x - 6y.

Now, he places y flowers (i.e., all flowers) in the shrine 3.

So, 8x - 6y = y, i.e., 8x = 7y or y = [latex]\frac{x}{y}[/latex] = [latex]\frac{7}{8}[/latex]

So, x and y are in the ratio 7 : 8.

Thus, if originally he was 7 flowers, he is placing 8 flowers at each shrine, if he has 14 flowers in the beginning, he is placing 16 flowers at each shrine, if he is having 21 flowers in the beginning, he is placing 24 flowers at each shrine, and so on. So, there are infinitely many solutions to this problem.