There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.

The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.

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Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.

i) The minimum among the numbers of coins in the three sacks in the box is 1.
ii) The median of the numbers of coins in the three sacks is 1.
iii) The maximum among the numbers of coins in the three sacks in the box is 9.

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What is the total number of coins in all the boxes in the 3rd row?

Question

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.

The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743486342/aptidude_questions/yncq1ykd1ke1h9adyzug.png)

Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.

i) The minimum among the numbers of coins in the three sacks in the box is 1.
ii) The median of the numbers of coins in the three sacks is 1.
iii) The maximum among the numbers of coins in the three sacks in the box is 9.

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What is the total number of coins in all the boxes in the 3rd row?

Accepted Answer

To calculate the total number of coins in all boxes in the third row:

1. **Understand constraints**:
   - Each box contains three sacks with distinct integers as averages.
   - The total number of coins in each row and column is equal.
   - From Tables 1 and 2, deduce sack distributions based on median and conditions.

2. **Determine sack values for boxes**:
   - Box (3,1): Average = $$8$$, meaning total coins = $$8 	imes 3 = 24$$. Sack values are $$7,8,9$$.
   - Box (3,2): Average = $$6$$, meaning total coins = $$6 	imes 3 = 18$$. Sack values are $$1,8,9$$.
   - Box (3,3): Average = $$1$$, meaning total coins = $$1 	imes 3 = 3$$. Sack values are $$1,1,1$$.

3. **Sum up totals**:
   - Total coins for row 3 = $$24 + 18 + 3 = 45$$.

Thus, **the total number of coins in all boxes in the third row is Rs. 45 lakhs**, making Option C correct.

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