Question

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.
How many flats did Neeta receive? ___

Answer 1

Refer to the table given below:
$\begin{array}{cccc}\text{Asset}& & & \\ \text{Flats (Rs.in lakhs)}& 30+30=60& & 30\\ \text{House (Rs.in lakhs)}& & 50& \\ \text{Bank deposits (Rs.in lakhs)}& x_1& x_2& 70-(x_1+x_2)\\ \text{Coins (Total number=n and)}& \frac{n}{3}& \frac{n}{3}& \frac{n}{3}\\ \text{Total value=n}\times 1=\text{Rs.n lakhs)}& & & \\ \text{Total (Rs. in lakhs)}& 60+x_1+\frac{n}{3}& 50+x_2+\frac{n}{3}& 30+70-(x_1+x_2)+\frac{n}{3}\end{array}$
Given, the total value of the assets is distributed equally among the three children. Then
$60+x_1+\frac{n}{3}=50+x_2+\frac{n}{3}=30+70-(x_1+x_2)+\frac{n}{3}$
Taking $60+x_1+\frac{n}{3}=50+x_2+\frac{n}{3}$, we get
$x_2-x_1=60-50=10-----------1)$
Now taking $50+x_2+\frac{n}{3}=30+70-(x_1+x_2)+\frac{n}{3}$, we get
$x_1+2x_2=50---------2)$
Putting the value of $x_2$ from 1) into 2), we get
$x_1+2(x_1+10)=503x_1=30$
$x_1=10$ lakhs
Hence, $x_2=20$ lakhs & $(70-x_1-x_2)=70–10–20=40$ lakhs
Since, it is given that Neeta received the least amount in bank deposits, therefore Neeta received $x_1$ = Rs. 10 lakhs in bank deposits, as Geeta received the highest deposits so, Geeta received Rs. 40 lakhs and Seeta received $x_2=20$ lakhs in bank deposits.
Hence, the updated table is as follows:
$\begin{array}{cccc}\text{Asset}& \text{Neeta}& \text{Seeta}& \text{Geeta}\\ \text{Flats (Rs.in lakhs)}& 30+30=60& & 30\\ \text{House (Rs.in lakhs)}& & 50& \\ \text{Bank deposits(Rs. in lakhs)}& 10& 20& 40\\ \text{Coins (Total number=n and)}& \frac{n}{3}& \frac{n}{3}& \frac{n}{3}\\ \text{Total value=n}\times \text{1=Rs.n lakhs)}& & & \\ \text{Total (Rs. in lakhs)}& 70+\frac{n}{3}& 70+\frac{n}{3}& 70+\frac{n}{3}\end{array}$
As can be seen from the table above, Neeta received 2 flats worth Rs. 30 lakhs each.