The price of an article increases by 5% every year. If the difference between its price at the end of the second and the third year is ₹52.50, then what will be its price at the end of the first year?

₹1,000

Let the initial price be 10000m

Increase = 5% = \(\frac{105}{100}\)

Price at the end of the first year = (10000m × \(\frac{105}{100}\) ) = 10500m

Price at the end of the second year = (10500m × \(\frac{105}{100}\)) = 11025m

Price at the end of the third year = (11025m × \(\frac{105}{100}\)) = 11576.25m

According to the question

11576.25m – 11025m = 52.50m

551.25m = 52.50

m = \(\frac{52.50}{551.25}\)

m = 0.0952

Price at the end of the first year = 10500m = (10500 × 0.0952) = 1000 Approx.