The price of commodity X increases by 40 paise every year, while the price of…
2024
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 Solution To determine the year in which commodity X costs 40 paise more than commodity Y, we can set up an algebraic equation based on the annual…
- A.
2010
- B.
2011
- C.
2056
- D.
2035
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Correct answer: B
Step-by-Step Solution
To determine the year in which commodity X costs 40 paise more than commodity Y, we can set up an algebraic equation based on the annual price increase.
Establish the initial prices in paise:
Initial price of commodity X (in 2001) = Rs. 4.20 = 420 paise.
Initial price of commodity Y (in 2001) = Rs. 6.30 = 630 paise.
Define the variables and annual increase:
Let 'z' be the number of years after 2001.
Annual increase for X = 40 paise/year.
Annual increase for Y = 15 paise/year.
Price of X after 'z' years = 420 + 40z.
Price of Y after 'z' years = 630 + 15z.
Set up the equation for the condition "X costs 40 paise more than Y":
(420 + 40z) - (630 + 15z) = 40
(420 - 630) + (40z - 15z) = 40
-210 + 25z = 40
25z = 40 + 210
25z = 250
z = 10 years.
Determine the final year:
The year = 2001 + 10 = 2011.