Discussion

Explanation:

As per the data given in the question the gold coins were equally distributed amongst the 3 children. We are also told that the remaining assets (apart from the gold coins) are also equally distributed and that no flat or house is split or divided between 2 or more people. Only the bank deposit of Rs.70 lakhs can be split. Apart from the gold coins, the total value of the assets is 70 + 50 + 30 + 30 + 30 = 210 lakhs

So 210 lakhs split equally would means that each of the 3 daughters would get Rs.70 lakhs. This would mean that the person receiving the Rs.50 lakh house would get Rs.20 lakhs from the bank deposit. Now there are 3 flats of Rs.30 lakhs each and a balance of 50 lakhs in the bank deposit. The only way these assets can be split equally is if one of the 2 remaining people gets one of the flats of Rs.30 lakhs and receives 40 lakhs from the bank deposit. The second person would receive 70-40-20 = 10 Lakhs as bank deposit and 2 flats of 30 lakhs each, the sum of which adds upto 70 lakhs.
As Neeta receives the least amount in bank deposits, she will receive 10 lakhs. Also, as Geeta receives the highest amount in bank deposits she wil receive 40 lakhs.

Let the total value of assets held by Neeta, Geeta and Seeta be x, 2x and 3x and the total number of gold coins held by each of them be 2y, 3y and 4y. So the total assets (apart from the gold coins) held by Neeta, Geeta and Seeta will be x – 2y, 2x – 3y and 3x – 4y. 

Now total assets apart from gold coin = 210 lakhs 

∴ (x – 2y) + (2x -3y) + (3x – 4y) = 210 

⇒ 6x – 9y = 210

On simplifying we get 2x – 3y = 70

This means that the total assets held by Geeta apart from the gold coins = 70 lakhs We are further told that one child got all 3 flats and one person other than Geeta got 30 lakhs in bank deposits. So then the only way Geeta could have got assets (other than gold coins) worth 70 lakhs is by getting the house of 50 lakhs and 20 lakhs from the bank deposit. This is also because all the 3 flats of Rs. 30 lakh each have gone to one person and obviously that person cannot be Geeta. This means that the 3rd sister has got 20 lakhs from the bank deposit (since one more sister has got 30 lakhs). Since Geeta cannot receive 30 lakhs from the bank deposit, it would imply that Neeta will receive 30 lakhs and Geeta will receive 20 lakhs from the bank deposit.
Now, all 3 flats go to either Neeta or Geeta.

If all 3 flats are received by Neeta, then the ratio of value of assets of Neeta and Geeta

(in terms of y) will be (30 + 90 + 2y): (20 + 4y)

 ⇒ (120 + 2y) : (20 + 4y) = $\frac{120+2y}{20+4y}$

$=\frac{1}{3}$

⇒ 360 + 6y = 20 + 4y ⇒ 2y = -340 or y = -170 

However ‘y’ cannot be a negative value. So all 3 flats will go to Geeta 

∴ Ratio of value of assets of Neeta and Geeta (in terms of y) will be (30 + 2y) : (20 + 90 + 4y) 

$\Rightarrow \frac{30+2y}{110+4y}=\frac{1}{3}$

⇒ 90 + 6y = 110 + 4y ⇒ y = 10 

Total number of gold coins = 2y + 3y + 4y = 9y = 90. 

Hence, option (b).

» Your doubt will be displayed only after approval.