A trader bought a consignment of potatoes and onions for Rs. 25,000. He sold the potatoes at a gain of 30% and the onions at a loss of 10%. If he gained 20% overall, how much did he pay for the potatoes?

Let's denote the cost of potatoes as P and the cost of onions as O. We know that P + O = Rs. 25,000.

We also know that the trader made a 20% overall gain, so he sold everything for 120% of the cost, which is 1.2 * Rs. 25,000 = Rs. 30,000.

He sold the potatoes at a 30% gain, so he sold them for 1.3P. He sold the onions at a 10% loss, so he sold them for 0.9O.

We can set up the equation 1.3P + 0.9O = Rs. 30,000.

We can substitute O from the first equation (O = Rs. 25,000 - P) into the second equation:

1.3P + 0.9(Rs. 25,000 - P) = Rs. 30,000.

Solving this equation will give us the cost of the potatoes (P).

Let's solve it:

1.3P + Rs. 22,500 - 0.9P = Rs. 30,000,

0.4P = Rs. 7,500,

P = Rs. 7,500 / 0.4 = Rs. 18,750.

So, the trader paid Rs. 18,750 for the potatoes.

Let's denote the cost of potatoes as P and the cost of onions as O. We know that P + O = 25,000 Rs.

We also know that the trader made a 20% overall gain, so he sold everything for 1.2 * 25,000 = 30,000 Rs.

The trader sold the potatoes at a 30% gain, so he sold them for 1.3P Rs. He sold the onions at a 10% loss, so he sold them for 0.9O Rs.

We can set up the equation 1.3P + 0.9O = 30,000 Rs.

We can solve this system of equations to find the values of P and O.

First, let's multiply the first equation by 1.3: 1.3P + 1.3O = 32,500 Rs.

Then, subtract the second equation from this new equation: 1.3P + 1.3O - 1.3P - 0.9O = 32,500 - 30,000 Rs.

This simplifies to 0.4O = 2,500 Rs.

So, O = 2,500 / 0.4 = 6,250 Rs.

Substitute O = 6,250 Rs into the first equation: P + 6,250 = 25,000 Rs.

So, P = 25,000 - 6,250 = 18,750 Rs.

Therefore, the trader paid 18,750 Rs for the potatoes.

Let's denote the cost of potatoes as P and the cost of onions as O. We know that P + O = Rs. 25,000.

We also know that the trader made a 20% overall gain, so he sold everything for 120% of the cost, which is 1.2 * Rs. 25,000 = Rs. 30,000.

He sold the potatoes at a 30% gain, so he sold them for 1.3P. He sold the onions at a 10% loss, so he sold them for 0.9O.

We know that the total selling price is the selling price of the potatoes plus the selling price of the onions, so we can write the equation 1.3P + 0.9O = Rs. 30,000.

We now have a system of two equations, and we can solve it step by step:

1. P + O = Rs. 25,000
2. 1.3P + 0.9O = Rs. 30,000

First, let's multiply the first equation by 1.3:

1.3P + 1.3O = Rs. 32,500

Now, let's subtract the second equation from this result:

1.3P + 1.3O - (1.3P + 0.9O) = Rs. 32,500 - Rs. 30,000

This simplifies to:

0.4O = Rs. 2,500

So, O = Rs. 2,500 / 0.4 = Rs. 6,250

Substitute O = Rs. 6,250 into the first equation:

P + Rs. 6,250 = Rs. 25,000

So, P = Rs. 25,000 - Rs. 6,250 = Rs. 18,750

So, the trader paid Rs. 18,750 for the potatoes.

Let's denote the cost of potatoes as P and the cost of onions as O. We know that P + O = Rs. 25,000.

We also know that the trader made a 20% overall gain, so he sold everything for 120% of the cost, which is 1.2 * Rs. 25,000 = Rs. 30,000.

The trader sold the potatoes at a 30% gain, so he sold them for 1.3P. He sold the onions at a 10% loss, so he sold them for 0.9O.

We can set up the equation 1.3P + 0.9O = Rs. 30,000.

We can substitute O = Rs. 25,000 - P from the first equation into the second equation to get 1.3P + 0.9(Rs. 25,000 - P) = Rs. 30,000.

Solving this equation for P gives us P = Rs. 15,000.

So, the trader paid Rs. 15,000 for the potatoes.