An old woman had the following assets:

(a) Rs. 70 lakh in bank deposits

(b) 1 house worth Rs. 50 lakh

(c) 3 flats, each worth Rs. 30 lakh

(d) Certain number of gold coins , each worth Rs. 1 lakh

She wanted to distribute her assets among her three children; Neeta, Seeta and Geeta. The house, any of the flats or any of the coins were not to be split. That is, the house went entirely to one child; a flat went to one child and similarly, a gold coin went to one child.

Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins.

**General Solution**

Let us compute the total asset base = This is Rs. 70 lakhs + Rs. 50 lakhs + Rs. 3 * 30 lakhs + n (Where number of gold coins is n).

Or, 210 lakhs + n is what the total asset base. This is equally distributed, or n should be a multiple of 3. So, let us rewrite n as 3m. Let us say the total asset base is 210 + 3m. Each child should get 70 + m. The gold coins were also equally distributed. This tells us that each child got m gold coins each. This makes life simple. Now, the non-gold coin part should have been equally distributed. So, each child should have gotten Rs. 70 lakhs worth stuff. What can we infer from here?

So, each child should have gotten Rs. 70 lakhs worth stuff.
1. Whoever gets the house cannot get a flat. Or, the person who gets the house should get Rs. 20 lakhs in cash.

2. No one can get all three flats. So, the flats get distributed as 1 and 2 to the two remaining children. So, one child gets House + Rs. 20 lakhs, one gets one flat plus Rs. 40 lakhs, and the third received two flats and Rs. 10 lakhs.

3. Beyond all this they receive an equal number of gold coins.

No one can get all three flats. So, the flats get distributed as 1 and 2 to the two remaining children. So, one child gets House + Rs. 20 lakhs, one gets one flat plus Rs. 40 lakhs, and the third received two flats and Rs. 10 lakhs.

Neeta receives 2 flats and Rs. 10 lakhs, Geeta receives one flat and Rs. 40 lakhs and Seeta gets house and Rs. 20 lakhs.

3. The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits.

How many gold coins did the old woman have?

A) 72

B) 90

C) 180

D) 216

Ans. The value of the assets were distributed in the ratio of 1:2:3. If we take them as 1x, 2x and 3x, then Total value = x + 2x + 3x = 6x.

If there are “m” gold coins, then the total 210 + m is a multiple of 6. 210 is a multiple of 6. So, m is a multiple of 6 => m = 6a.

Also, the gold coins were distributed in the ratio of 2:3:4 => No. of gold coins is 2y +3y + 4y = 9y.
m = 9y .

m is a multiple of 6 and 9.Therefore, m is a multiple of 18. Hence, m can be expressed as 18k for some k.
Now, total value of assets = 210 + 18k. This is split in the ratio of 1:2:3 among Neeta, Seeta and Geeta.

Neeta gets = * (210 + 18K) = 35 + 3k = (35 – k ) + 4k.

Seeta gets = * (210 + 18K) = 70 + 6k.

Geeta gets = * (210 + 18K) = 105 + 9k = (105 + k ) + 8k.

We also know that, One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits.

One of Seeta and Neeta got Rs. 30 lakh in bank deposits.

Seeta could not have got Rs. 30 lakh in bank deposits. Because, if she got Rs. 30 lakhs. Then the remaining amount she will have is 40 + 6k which is not possible through any combination.

Hence, Neeta gets Rs. 30 lakh in bank deposits.Neeta got totally (35 – k ) + 4k worth of assets. So, k = 5.
Neeta gets Rs. 30 lakh in bank deposits and 4*5 = 20 gold coins.

Seeta gets one house and Rs. 20 lakh in bank deposits and 30 gold coins.

Geeta gets 3 flats and Rs. 20 lakh in bank deposits and 40 gold coins.

Therefore, total no. of gold coins = 20 + 30 + 40 = 90.

Answer choice (B).

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