The price of commodity X increases by 40 paise every year, while the price of…
2023
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
Answer: B. 2011 — Step-by-Step SolutionTo find the year in which the price of commodity X will be 40 paise more than commodity Y, we can set up an equation based on the number…
- A.
2020
- B.
2011
- C.
2098
- D.
2145
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
To find the year in which the price of commodity X will be 40 paise more than commodity Y, we can set up an equation based on the number of years passed.
Define the variables:
Let n be the number of years after 2001.
Commodity X price in 2001 = Rs. 4.20 = 420 paise.
Commodity Y price in 2001 = Rs. 6.30 = 630 paise.
Annual increase for X = 40 paise.
Annual increase for Y = 15 paise.
Set up the equation for the price after n years:
Price of X after n years = 420 + 40n
Price of Y after n years = 630 + 15n
Apply the condition (X = Y + 40):
(420 + 40n) = (630 + 15n) + 40
420 + 40n = 670 + 15n
40n - 15n = 670 - 420
25n = 250
n = 10
Determine the year:
The year = 2001 + 10 = 2011.