Question

The number of goats the youngest son received was:

• A. 15
• B. 18
• C. 12
• D. 10
• A. Rupees7,75,000
• B. Rupees6,25,000
• C. Rupees6,75,000
• D. Rupees7,25,000
• A. 30
• B. 35
• C. 20
• D. 25
• A. 560
• B. 580
• C. 540
• D. 520

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the number of goats received by the youngest son (the fourth son).
Scenario Breakdown:
Let the total wealth of the shepherd be 'W'. The wealth is distributed equally among four sons, so each son's share is W/4.

Eldest Son's Share: The eldest son received sheep worth 20% of the total worth (0.2W) and Rupees 33,750 in cash. \[ \frac{W}{4} = 0.2W + 33,750 \] \[ 0.25W - 0.2W = 33,750 \] \[ 0.05W = 33,750 \] \[ W = \frac{33,750}{0.05} = 675,000 \] The total wealth is Rupees 6,75,000. Each son's share is \( \frac{675,000}{4} = \text{Rupees} 1,68,750 \).
Eldest Son's Details: Sheep worth = 0.2 \(\times\) 675,000 = Rupees 1,35,000. Cash = Rupees 33,750. Total = Rupees 1,68,750.
Second Son's Details: The remaining worth after the first son is \( W - \frac{W}{4} = \frac{3W}{4} = 506,250 \). He received goats worth 20% of this remaining worth. Goats worth = 0.2 \(\times\) 506,250 = Rupees 1,01,250. Cash = Rupees 67,500. Total = 1,01,250 + 67,500 = Rupees 1,68,750. (This matches)
Third and Fourth Sons' Details: The remaining worth after the second son is \( 506,250 - 1,68,750 = \text{Rupees}3,37,500 \). Their total share is \( 2 \times 1,68,750 = \text{Rupees}3,37,500 \), which matches the remaining amount. The cash for each was Rupees33,750 more than the second son: Rupees 67,500 + Rupees 33,750 = Rupees 1,01,250. The value of cattle for each son is their total share minus cash: Rupees 1,68,750 - Rupees 1,01,250 = Rupees 67,500. They received an equal number of sheep (s) and goats (g), so s = g. \[ s \times 5400 + g \times 1350 = 67,500 \] \[ g \times (5400 + 1350) = 67,500 \] \[ g \times 6750 = 67,500 \implies g = 10 \] So, the third and fourth sons each received 10 sheep and 10 goats.
Step 2: Key Formula or Approach:
Based on our initial breakdown of the scenario, the youngest son received cattle worth Rupees67,500, consisting of an equal number of sheep and goats. Let 'n' be the number of sheep and also the number of goats. Value of 1 sheep = Rupees5,400.
Value of 1 goat = Rupees1,350.
\[ n \times (\text{Value of sheep}) + n \times (\text{Value of goat}) = \text{Total Cattle Value} \] Step 3: Detailed Explanation:
\[ n \times 5,400 + n \times 1,350 = 67,500 \] \[ n \times (5,400 + 1,350) = 67,500 \] \[ n \times 6,750 = 67,500 \] \[ n = \frac{67,500}{6,750} = 10 \] So, the youngest son received 10 goats (and 10 sheep).
Step 4: Final Answer:
The number of goats the youngest son received was 10.

Answer 2

Step 1: Understanding the Question:
The question asks for the total wealth (cash + cattle) of the shepherd before any distribution.
Step 2: Key Formula or Approach:
We can determine the total wealth (W) from the information given for the eldest son. The share of each son is W/4. The eldest son's share is also given as (20% of W) + Rupees33,750. By equating these, we can solve for W.
\[ \frac{W}{4} = 0.20W + 33,750 \] Step 3: Detailed Explanation:
\[ 0.25W = 0.20W + 33,750 \] \[ 0.25W - 0.20W = 33,750 \] \[ 0.05W = 33,750 \] \[ W = \frac{33,750}{0.05} \] \[ W = 6,75,000 \] Step 4: Final Answer:
The shepherd had a total wealth of Rupees6,75,000 before the distribution.

Answer 3

Step 1: Understanding the Question:
We need to find the number of sheep received by the eldest son.
Step 2: Key Formula or Approach:
From our initial calculations, we know the total wealth was Rupees6,75,000. The eldest son received sheep worth 20% of this total wealth.
\[ \text{Number of sheep} = \frac{\text{Total value of sheep received}}{\text{Value of one sheep}} \] Step 3: Detailed Explanation:
Total value of sheep for the eldest son = 20% of Rupees6,75,000
\[ \text{Value} = 0.20 \times 675,000 = \text{Rupees}1,35,000 \] The value of one sheep is Rupees5,400.
\[ \text{Number of sheep} = \frac{135,000}{5,400} = \frac{1350}{54} = 25 \] Step 4: Final Answer:
The eldest son received 25 sheep.

Answer 4

Step 1: Understanding the Question:
The question asks for the total number of legs of all the sheep and goats combined. Since both sheep and goats have 4 legs, we need to find the total number of animals.
Step 2: Key Formula or Approach:
1. Find the number of sheep and goats each son received.
2. Sum them up to get the total number of cattle.
3. Multiply the total number of cattle by 4.
Step 3: Detailed Explanation:
Eldest son: 25 sheep (from Q.23), 0 goats.
Second son: Received goats worth Rupees1,01,250. Value of one goat is Rupees1,350.
Number of goats = \( \frac{101,250}{1,350} = 75 \) goats. 0 sheep.
Third son: 10 sheep, 10 goats (from Q.21).
Youngest son: 10 sheep, 10 goats (from Q.21).
Total number of cattle:
Total sheep = 25 + 0 + 10 + 10 = 45 sheep.
Total goats = 0 + 75 + 10 + 10 = 95 goats.
Total animals = 45 + 95 = 140 animals.
Total number of legs:
\[ \text{Total legs} = \text{Total animals} \times 4 = 140 \times 4 = 560 \] Step 4: Final Answer:
The total number of legs of all the cattle is 560.