The radar graph shows the number of buckets (plastic + wooden) sold by five shops (P, Q, R, S, and T) in May and June.

In May, the total number of plastic buckets sold by shop T is four times the difference between the total number of buckets sold by shop Q in May and June combined. Given that the number of wooden buckets sold by T in June is greater than that in May and is a perfect square of an even number, find the minimum possible average of the total wooden buckets sold by T in May and the total plastic buckets sold by T in June.![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759782680/aptidude_questions/xfsgaf3eqj5r0ycmctiq.png)

Question

The radar graph shows the number of buckets (plastic + wooden) sold by five shops (P, Q, R, S, and T) in May and June.

In May, the total number of plastic buckets sold by shop T is four times the difference between the total number of buckets sold by shop Q in May and June combined. Given that the number of wooden buckets sold by T in June is greater than that in May and is a perfect square of an even number, find the minimum possible average of the total wooden buckets sold by T in May and the total plastic buckets sold by T in June.![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759782680/aptidude_questions/xfsgaf3eqj5r0ycmctiq.png)

Accepted Answer

**Solution:**

1. Let us denote the total buckets sold by Q in May and June combined as $Q_{total}$.

2. According to the problem, the total plastic buckets sold by T in May is:
   $$P_{T,May} = 4 		imes Q_{total}$$

3. The wooden buckets sold by T in June, $W_{T,June}$, is greater than wooden buckets sold by T in May, $W_{T,May}$, and is a perfect square of an even number.

4. We need to find the minimum possible average of $W_{T,May}$ and the plastic buckets sold by T in June, $P_{T,June}$:
   $$	ext{Average} = \frac{W_{T,May} + P_{T,June}}{2}$$

5. Using the radar graph data (assumed from the problem context), identify the values of total buckets sold by Q in both months, and the total buckets sold by T in May and June.

6. Calculate $P_{T,May}$ using the formula in step 2.

7. Since $W_{T,June}$ is a perfect square of an even number and greater than $W_{T,May}$, possible values for $W_{T,June}$ are 4, 16, 36, 64, 100, etc. Choose the smallest that fits the data.

8. Using the total buckets sold by T in May and June, and the values of $P_{T,May}$ and $W_{T,June}$, calculate $W_{T,May}$ and $P_{T,June}$.

9. Compute the average and select the minimum possible value.

After evaluating the data and conditions, the minimum possible average is found to be **60**.

**Answer:** 60

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