Question

the cost of two varieties of paint is rs.3969 per 2 kg and rs.1369 per 2 kg respectively. after how many years the value of both paint will be the same if variety 1 appreciates at 26% per annum and variety 2 depreciates at 26% per annum?

Answer 1

Answer: 2 years

Explanation:

Variety 1 appreciates by 26% per annum while Variety 2 depreciates by 26% per annum.

Variety 1 current price: Rs. 3,969

Variety 1 appreciates: Rs. 3,969 × (1 - 0.26)^n

Variety 2 current price: Rs. 1,369

Variety 2 depreciates: Rs. 1,369 × (1 + 0.26)^n

The year in which both will be equal :

Rs. 3,969 × (1 - 0.26)^n = Rs. 3,969 × (1 + 0.26)^n

By using trial and error method, let n = 2 and solve the above equation:

Rs. 3,969 × (0.74)^2 = Rs. 2,173.43

Rs. 1,369 × (1.26)^2 = Rs. 2,173.43

Rs. 2173.43 = Rs. 2173.43

By using trial and error method, at n = 2, the variety 1 and variety 2 prices are equal. Therefore answer is 2.