A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below:

The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known:

1. Abha got 20 trees more than Chitra but 6 trees less than Dipti.
2. The largest number of trees in a plot was 32, but it was not with Abha.
3. The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.
4. Both Abha and Bina got a higher number of plots than Dipti.
5. Only Bina, Chitra and Dipti got corner plots.
6. Dipti got two adjoining plots in the same row.
7. Bina was the only one who got a plot in each row and each column.
8. Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).
9. The number of mango trees was double the number of teak trees.

How many mango trees were there in total?

The correct answer is 98.

To find the total number of mango trees, let us analyze the grid structure and the numerical data provided in the image:
1. Row X represents Mango trees.
2. Row Y represents Teak trees.
3. Row Z represents Pine trees.
From the given image, we can identify the following initial values and ownership labels in the plots:
- Plot (X, 1) has 12 trees and is allocated to Chitra (C).
- Plot (Y, 1) has 21 trees and is allocated to Abha (A).
- Plot (Y, 4) is allocated to Abha (A), but the number of trees is erased.
- Plot (Z, 1) is allocated to Bina (B).
- Plot (Z, 2) is allocated to Chitra (C).
- Plot (Z, 3) has 9 trees.
- Plot (Z, 4) has 28 trees.

According to Rule 3, the number of teak trees (Row Y) in Column 3 is double that in Column 2, and half of that in Column 4. Let the number of teak trees in plot (Y, 2) be represented as:

$Y_2=k$

Then, the teak trees in Column 3 and Column 4 are:

$Y_3=2k$

$Y_4=4k$

Since the number of trees in each plot must be a non-zero multiple of 3 or 4, and the maximum number of trees in any plot is 32, we know that:

$Y_4=4k\le 32$

Additionally, all 12 plots must have distinct numbers of trees. The values already used in the grid are 9, 12, 21, and 28. Let us test the possible integer values for $k$ such that $k$, $2k$, and $4k$ are distinct multiples of 3 or 4:
- If $k=3$, then the values are 3, 6, and 12. However, 12 is already present in plot (X, 1). Thus, $k\ne 3$.
- If $k=8$, then the values are 8, 16, and 32. This would mean plot (Y, 4) has 32 trees. However, the image shows that plot (Y, 4) is allocated to Abha (A). Rule 2 states that the plot with the largest number of trees (32) was not with Abha. Thus, $k\ne 8$.
- If $k=4$, then the values are 4, 8, and 16. None of these values conflict with the existing numbers (9, 12, 21, 28) and all are valid multiples of 4 or 8.

Therefore, we find that:

$Y_2=4$

$Y_3=8$

$Y_4=16$

Since plot (Y, 1) has 21 trees, we can calculate the total number of teak trees in Row Y:

$\text{Total Teak Trees}=21+4+8+16=49$

According to Rule 9, the number of mango trees (Row X) is double the number of teak trees (Row Y):

$\text{Total Mango Trees}=2\times 49=98$