The problem provided is about the total number of coins and the total value of those coins. Here's the summary:

• Total coins: 400
• Total money: ₹1568
• The coins are in denominations of ₹1, ₹2, ₹5, and ₹10.

Conditions:

1. The number of ₹10 coins is half the number of ₹5 coins.
2. The number of ₹5 coins is one-third the number of ₹1 coins.
3. The number of ₹2 coins is one-fourth the number of ₹1 coins.

Requirements:

1. Find the number of ₹1 and ₹2 coins used for food.
2. Find the number of ₹5 coins used for the party.
3. Find the total money spent on food and the total money used for the party.

Let’s define the variables:

• Let $x$ be the number of ₹1 coins.
• From the conditions given:
  • ₹5 coins: $\frac{x}{3}$
  • ₹10 coins: $\frac{x}{6}$
  • ₹2 coins: $\frac{x}{4}$

Using this setup, we can proceed to form equations and solve for each case.

I'll work on solving the system of equations.It seems like the system of equations doesn't have a straightforward solution with the assumptions made. Let me recheck the constraints and simplify the problem setup again.

The key steps involve ensuring that the total number of coins sums to 400 and their value sums to ₹1568 while respecting the conditions about the relationships between the coins.

I will try solving this problem using a refined approach.Let me refine the setup of the problem based on the relationships provided.

1. Let $x$ be the number of ₹1 coins.
2. The number of ₹2 coins is $\frac{x}{4}$.
3. The number of ₹5 coins is $\frac{x}{3}$.
4. The number of ₹10 coins is $\frac{x}{6}$.

Total coins:

$x + \frac{x}{4} + \frac{x}{3} + \frac{x}{6} = 400$

Total money:

$1(x) + 2\left(\frac{x}{4}\right) + 5\left(\frac{x}{3}\right) + 10\left(\frac{x}{6}\right) = 1568$

I'll solve this new system to find $x$, the number of ₹1 coins.It appears there is still no straightforward solution from this approach. This could be due to inconsistencies in the given relationships or assumptions. Let me double-check the setup and consider alternate ways to solve it.

I'll review and refine the relationships or relax some constraints, ensuring all conditions are met to arrive at the correct solution. Would you like to proceed with an assumption-based calculation or clarify the problem further?