Question

The price of Darjeeling Tea (in rupees per kilogram) is \(100 + 0.1n\), on the nth day of a nonleap year \((n = 1, 2, 3, ... 100)\) and then remains constant. On the other hand the price of Ooty tea (in rupees per kilogram) is \(85 + 0.15n\), on the nth day \((n = 1, 2, ..., 365)\). On which date of that year will the prices of these two varieties of the tea be equal?

• A. 27^th October
• B. 16^th June
• C. 15^th June
• D. 28^th October

Answer 1

The Correct Option is B

To find the date when the prices of Darjeeling Tea and Ooty Tea are equal, we need to solve for n in the price equations of both teas.

The price of Darjeeling Tea on the nth day is given by: 

\(P_D = 100 + 0.1n\)

For the first 100 days, the price varies. After that, it remains constant at \(110\) rupees (since \(P_D = 100 + 0.1 \times 100 = 110\) for \(n>100\)).

The price of Ooty Tea on the nth day is given by:

\(P_O = 85 + 0.15n\)

We need to find the day when both prices are equal:

\(100 + 0.1n = 85 + 0.15n\)

Rearranging the equation by subtracting \(85 + 0.1n\) from both sides, we get:

\(15 = 0.05n\)

Solving for n, we divide both sides by \(0.05\):

\(n = \frac{15}{0.05} = 300\)

The 300th day of the year is June 16th in a non-leap year. Thus, the prices of Darjeeling Tea and Ooty Tea become equal on this date.

Answer: 16^th June