The cost of two varieties of paint is rupees 1369 per 2kg and rupees 3969 per…
2023
The cost of two varieties of paint is rupees 1369 per 2kg and rupees 3969 per 2 kg respectively, after how many years will the value of both paint be the same if variety 1 appreciates at 26% per annum and variety 2 depreciates at 26% per annum?
- A.
6 years
- B.
4 years
- C.
2 years
- D.
3 years
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept: When an amount P appreciates at R% per annum, its value after n years is P(1 + R/100)n. When an amount P depreciates at R% per annum, its value after n years is P(1 − R/100)n — the same compounding idea as compound interest, but with a negative growth rate for depreciation.
Variety 1 (cost 1369) appreciates at 26% per annum, so its value after n years is 1369(1 + 26/100)n = 1369(126/100)n.
Variety 2 (cost 3969) depreciates at 26% per annum, so its value after n years is 3969(1 − 26/100)n = 3969(74/100)n.
Equate the two values (the 100n in the denominators cancels on both sides): 1369(126)n = 3969(74)n, i.e. (126/74)n = 3969/1369.
Simplify both sides: 126/74 reduces to 63/37, and since 632 = 3969 and 372 = 1369, the right side 3969/1369 is exactly (63/37)2.
So the equation becomes (63/37)n = (63/37)2, and since the bases are equal and greater than 1, the exponents must match: n = 2.
Cross-check: At n = 2, variety 1's value is 1369 × (126/100)2 = 2173.4244 and variety 2's value is 3969 × (74/100)2 = 2173.4244 — the two values match exactly, confirming n = 2 years.
