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At the start of the year the total value of land and building together is Rs. 20,00,000. During the year value of land increases by 30% and the value of the building decreases by 20%. If at the end of the year, the value of land and the building together becomes Rs. 22,00,000, find the value of the land at the start of the year.

Question

At the start of the year the total value of land and building together is Rs. 20,00,000. During the year value of land increases by 30% and the value of the building decreases by 20%. If at the end of the year, the value of land and the building together becomes Rs. 22,00,000, find the value of the land at the start of the year.

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Solution

Let's denote the initial value of the land as L and the initial value of the building as B. We know from the problem that:

L + B = 20,00,000 (equation 1)

During the year, the value of the land increases by 30% and the value of the building decreases by 20%. So, at the end of the year, the total value is:

1.3L + 0.8B = 22,00,000 (equation 2)

Now we have a system of two equations, and we can solve it step by step.

First, let's express B from equation 1:

B = 20,00,000 - L

Now we can substitute B in equation 2:

1.3L + 0.8*(20,00,000 - L) = 22,00,000

Let's simplify this equation:

1.3L + 16,00,000 - 0.8L = 22,00,000

0.5L = 6,00,000

Finally, we can find the value of L:

L = 6,00,000 / 0.5 = 12,00,000

So, the value of the land at the start of the year was Rs. 12,00,000.

This problem has been solved

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