Question

How much did Seeta receive in bank deposits (in lakhs of rupees)?

• A. 30
• B. 40
• C. 20
• D. 10
• A. 72
• B. 90
• C. 180
• D. 216

Answer 1

The Correct Option is C

Step 1: Total asset value

Given:

• Bank deposits = ₹ 70 lakh
• House = ₹ 50 lakh
• 3 Flats (₹ 30 lakh each) = ₹ 90 lakh
• Gold coins = \( x \) lakh (₹ 1 lakh each)

Total asset value: \[ \text{Total} = 70 + 50 + 90 + x = (210 + x) \ \text{lakh} \]

Step 2: Equal share per person

Each of the three children receives: \[ \frac{210 + x}{3} \ \text{lakh} \]

Step 3: Distribution rules

• House, flats, and coins are indivisible.
• Neeta gets the least bank deposits.
• Geeta gets the most bank deposits.

Step 4: Example allocation

Assign:

• House (₹ 50 lakh) to Geeta.
• Remaining ₹ 60 lakh in flats distributed among Neeta and Seeta.
• Gold coins equally shared: assume \( x = 9 \) coins → ₹ 9 lakh total value → ₹ 3 lakh per child.

Step 5: Equal share calculation

If \( x = 9 \), total value = \( 210 + 9 = 219 \) lakh. Each child’s share: \[ \frac{219}{3} = 73 \ \text{lakh} \]

Step 6: Detailed distribution

• Geeta: House (₹ 50 lakh) + ₹ 23 lakh bank deposits + 3 coins (₹ 3 lakh) Total = \( 50 + 23 + 3 = 76 \) lakh → requires adjustment with flats/coins for exact ₹ 73 lakh.
• Seeta: 1 flat (₹ 30 lakh) + ₹ 20 lakh bank deposits + 3 coins (₹ 3 lakh) + balance from remaining flats to total ₹ 73 lakh.
• Neeta: Remaining flats, coins, and bank deposits to make up ₹ 73 lakh, with least bank deposits.

Step 7: Key result

From the balance equations and constraints, Seeta’s bank deposits are: \[ \boxed{\text{₹ 20 lakh}} \]

Answer 2

Step 1: Total assets

Assets	Value (₹ lakh)
Bank Deposits	70
House	50
3 Flats	90
Gold Coins	C

Total asset value: \[ \text{Total} = 70 + 50 + 90 + C = (210 + C) \ \text{lakh} \]

Step 2: Equal share per person

Neeta, Seeta, and Geeta each receive: \[ \frac{210 + C}{3} \ \text{lakh} \]

Step 3: Bank deposit allocation

Let Neeta’s bank deposit = \( x \) lakh, Geeta’s = \( y \) lakh. We have: \[ x < y \quad\text{and}\quad x + y = 70 \] The middle share (Seeta) is automatically \( 70 - (x + y) \) adjusted by assets.

Step 4: Gold coin allocation

Gold coins are equally divided: \[ \text{Coins per person} = \frac{C}{3} \ \text{lakh} \]

Step 5: Asset value equations

Let \( F_N, F_S, F_G \) be the value from flats/houses each person gets: \[ V_N = x + F_N + \frac{C}{3} \] \[ V_S = \text{(Bank share)} + F_S + \frac{C}{3} \] \[ V_G = y + F_G + \frac{C}{3} \] and \[ V_N = V_S = V_G = \frac{210 + C}{3} \]

Step 6: Flats value and minimum allocation

Each flat is worth: \[ \frac{90}{3} = 30 \ \text{lakh} \] To balance her low bank deposit, Neeta must receive a higher value in property.

Step 7: Conclusion from constraints

Under equal distribution:

• Neeta gets the least bank deposit.
• Gold coins are equally distributed.
• Her remaining share must be made up with property value.
• Minimum needed for balance = 2 flats worth \( 60 \ \text{lakh} \).

 

Final Answer:

\[ \boxed{\text{Neeta received 2 of the 3 flats.}} \]

Answer 3

An old woman's total assets are: 

• Bank deposits: Rs. 70 lakhs
• House: Rs. 50 lakhs
• 3 flats: Rs. 90 lakhs (each flat Rs. 30 lakhs)
• Certain gold coins: each worth Rs. 1 lakh

Total value of assets = Rs. 70 + Rs. 50 + Rs. 90 + x (gold coins)= Rs. 210 + x lakhs. She distributed the assets equally among her three children, Neeta, Seeta, and Geeta. Therefore, the amount each child received = (Rs. 210 + x)/3 lakhs. Let's denote the number of gold coins as 'n'. Therefore, their total worth is Rs. n lakhs. Each child's share must be an integer since individual items like the house, flats, or coins cannot be divided. Since the house is indivisible, it entirely goes to one of the children, contributing Rs. 50 lakhs to that child. Similarly, each flat contributes Rs. 30 lakhs to a child's share. Let's consider various combinations:

1. The house can go to only one child.
2. Each flat goes similarly to one child.

If Neeta receives the house (Rs. 50 lakhs) and one flat (Rs. 30 lakhs), this would account for Rs. 80 lakhs of assets. Another Rs. 70/3 lakhs would leave Neeta with a non-integral share. Geeta, receiving the highest from bank deposits, gets Rs. 70 lakhs and one flat (Rs. 30 lakhs), totaling Rs. 100 lakhs. Hence, Geeta could receive no gold coins. Seeta must then receive Rs. 100 lakhs in total assets (Rs. 50 lakhs house + Rs. 30 lakhs flat + Rs. 20 lakhs total in gold coins).

• For this: Total coins contribution = 3n lakhs.

Thus,

Neeta	House (50) + Flat (30) + Coins (y)
Seeta	Flat (30) + Coins (y)
Geeta	Bank Deposits (70) + Flat (30)

Solving: y + y + Coins = Gold Coins = 3(y) = 3x. Solving equality gives x = 90, meaning there are 90 coins in total worth Rs. 90 lakhs.

Answer 4

The old woman has the following assets to distribute among her children: Neeta, Seeta, and Geeta.

Total bank deposits: ₹70 lakh 

Total house(s) value: ₹50 lakh

Total flats value: ₹90 lakh (3 flats × ₹30 lakh each)

Let the number of gold coins be x (each worth ₹1 lakh).

The total value of assets is ₹70 lakh (bank deposits) + ₹50 lakh (house) + ₹90 lakh (flats) + ₹1 lakh × x (gold coins).

Given that the assets were distributed equally among the children:

Total value = 210 + x lakhs.

Each child gets = (210 + x)/3 lakhs.

Each received an integer number of gold coins, so x must be divisible by 3. Thus, let x be 3k for some integer k. The total value each child receives becomes (210 + 3k)/3 lakhs = 70 + k.

Now, allocate assets:

• Neeta received the least in deposits.
• Geeta received the highest in deposits.

Assign other assets:

• Geeta can be given the house (₹50 lakh) and 1 flat (₹30 lakh) = ₹80 lakh.
• Neeta can get 2 flats (2 × ₹30 lakh) = ₹60 lakh.
• Thus, Seeta gets no house or flats, meaning she gets only gold coins and deposits.

Given each gets (70 + k) lakhs:

• Geeta: ₹80 lakh + deposits = 70 + k → deposits = (70 + k - 80) = k - 10 lakh (since k > 10 to satisfy deposit balance).
• Neeta: ₹60 lakh + deposits = 70 + k → deposits = k + 10 lakh.
• Seeta: Gold coins worth (70 + k) - bank deposits.

Choose values for k:

 

Let k = 20 (as derived from distribution):

• Deposit for Geeta = 20 - 10 = ₹10 lakh.
• Deposit for Neeta = 20 + 10 = ₹30 lakh.
• Deposit for Seeta = ₹70 lakh (from summation constraining them to equalized values and Carried forward values mentioned above)

Now verify distributions within balance:

• Geeta receives: ₹80 (assets) + ₹10 deposits
• Neeta receives: ₹60 (assets) + ₹30 deposits
• Together, children received: ₹210 + 20 lakh, confirming deposit totals and balances.

Thus, Geeta receives ₹20 lakh in bank deposits.