Question

Radha takes some flowers in a basket and visits three temples one by one. At each temple, she offers one half of the flowers from the basket. If she is left with 3 flowers at the end, find the number of flowers she had in the beginning.

Answer 1

Hint:
Here we will first assume the number of flowers in the basket in the beginning to be some variable. Then we will use the condition given to find the number of flowers left after visit to the third temple. We will then equate the number of flowers left to 3 and solve it to get the number of flowers she had in the beginning.

Complete step by step solution:
Let us assume the number of flowers in the basket in the beginning be \[x\].
It is given that at each temple, she offers one half of the flowers from the basket.
Now we will write the number of flowers left after visiting the first temple. Therefore, we get
Number of flowers left after the visit of the first temple \[ = \dfrac{x}{2}\]
Now we will find the number of flowers left after visiting the second temple. So, we get
Number of flowers left after the visit of the second temple \[ = \dfrac{x}{4}\]
Similarly, Number of flowers left after the visit of the third temple \[ = \dfrac{x}{8}\]
It is given that she is left with 3 flowers at the end which means
 \[ \Rightarrow \dfrac{x}{8} = 3\]
Now by solving this we will get the number of flowers in the basket in the beginning.
Multiplying both sides by 8, we get
 \[ \Rightarrow x = 3 \times 8\]
Again multiplying the terms, we get
 \[ \Rightarrow x = 24\]

Hence the number of flowers she had in the beginning is 24.

Note:
We can also find it by the reverse concept i.e. multiplying 2 to the number of flowers left at the end to get the number of flowers she had before the third temple visit.
Number of flowers before the visit of third temple \[ = 2 \times 3 = 6\]
Again, Multiplying 2 to 6 we will get the number of flowers she had before the second temple visit.
Number of flowers before the visit of second temple \[ = 2 \times 6 = 12\]
Then, similarly, for the first temple to get the number of flowers she had in the beginning we will multiply 12 to 2.
Number of flowers before the visit of first temple \[ = 2 \times 12 = 24\]
Hence, the number of flowers she had in the beginning is 24.