Question

A person buys 18 local tickets for Rs. 110. Each first class ticket costs Rs. 10 and each second class ticket costs Rs. 3. What will another lot of 18 tickets in which the number of first class and second class tickets are interchanged cost?

• A. 112
• B. 118
• C. 121
• D. 124

Answer 1

The Correct Option is D

A person buys 18 tickets for Rs. 110 where each first class ticket costs Rs. 10 and each second class ticket costs Rs. 3. Let us consider the number of first class tickets as x and the number of second class tickets as y. Therefore, the following equations can be set up based on the given information:

1. \(x + y = 18\)

2. \(10x + 3y = 110\)

Using equation 1, we can express y in terms of x:

\(y = 18 - x\)

Now substitute y in equation 2:

\(10x + 3(18 - x) = 110\)

\(10x + 54 - 3x = 110\)

\(7x = 110 - 54\)

\(7x = 56\)

\(x = 8\)

So, the number of first class tickets is 8 and therefore, the number of second class tickets y is:

\(y = 18 - 8 = 10\)

Now, to find the cost when the number of first class and second class tickets are interchanged, the number of first class tickets is 10 and the number of second class tickets is 8. The total cost will be:

\(10 \times 10 + 3 \times 8 = 100 + 24 = 124\)

Thus, the cost of the interchanged tickets is Rs. 124.