A father has Rs. 2000 and wants to distribute this amount among his five children so that each child receives Rs. 30 more than the next younger child. What is the share of the youngest child?

Introduction / Context:
This question involves distribution of money among children in arithmetic progression. Each older child receives a fixed amount more than the next younger child, and the total is known. Such problems are good practice for arithmetic progressions and basic algebraic equations used in aptitude exams.

Given Data / Assumptions:

• Total money to be distributed = Rs. 2000.
• There are 5 children.
• Each child gets Rs. 30 more than the immediately younger child.
• The youngest child gets the smallest share.

Concept / Approach:
The shares form an arithmetic progression because the difference between consecutive terms is constant. If we let the youngest child share be x, then the shares of the others are x + 30, x + 60, x + 90 and x + 120. We sum this progression, set equal to the total, and solve for x.

Step-by-Step Solution:
Step 1: Let the youngest child share be x rupees.Step 2: Then the second youngest gets x + 30, then x + 60, x + 90 and the oldest gets x + 120.Step 3: Total money distributed = x + (x + 30) + (x + 60) + (x + 90) + (x + 120).Step 4: Combine like terms: total = 5x + (30 + 60 + 90 + 120) = 5x + 300.Step 5: Set equal to 2000: 5x + 300 = 2000.Step 6: Subtract 300: 5x = 1700, so x = 1700 / 5 = 340.

Verification / Alternative check:
Check the individual shares: youngest 340, then 370, 400, 430 and oldest 460. Sum = 340 + 370 + 400 + 430 + 460 = 2000. This matches the total amount available, confirming that the distribution is consistent and that the youngest child share is correct.

Why Other Options Are Wrong:
Shares like Rs. 280 or Rs. 310 would give totals smaller than 2000 when you build the progression. Rs. 360 or Rs. 400 as shares for the youngest child would produce a sum larger than 2000 for the five children when you add the extra steps of 30 rupees each.

Common Pitfalls:

• Placing x for the middle child instead of the youngest child, which shifts the progression and gives a wrong equation.
• Adding the constant difference incorrectly and miscomputing the fixed sum 30 + 60 + 90 + 120.
• Making a calculation error when dividing 1700 by 5.

Final Answer:
The share of the youngest child is Rs. 340.