Simplification with equal sharing: When a fixed amount is shared among 14 girls, each receives ₹160 more than she would if the same amount were equally shared among 18 girls. Find the total amount.

Introduction / Context:
In this quantitative aptitude problem on equal distribution, the same sum of money is shared among two different group sizes. Because the group of 14 is smaller than the group of 18, the per-person share increases by a fixed amount. We use unitary method or simple algebra to compute the total amount.

Given Data / Assumptions:

• Total amount = A (unknown)
• Share with 14 girls = A/14
• Share with 18 girls = A/18
• Increase per girl when there are 14 instead of 18 = ₹160

Concept / Approach:
When the same amount is divided among fewer people, each person gets more. The difference between the two per-person amounts equals ₹160. Set up a linear equation in A and solve.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 5040: Half of the correct total; would not yield a ₹160 difference.
• ₹ 10070: Close but incorrect; difference would not be exactly ₹160.
• ₹ 5000: Too small to produce the stated per-person increase.

Common Pitfalls:

• Adding 160 directly to the total rather than to the per-person share.
• Computing 1/18 - 1/14 instead of 1/14 - 1/18, which flips the sign.

Final Answer: