Question

The cost of an I-pad increases by 10% and the cost of a mobile increases by 18%. The cost of an I-pad is thrice the cost of a mobile. Find the percentage increase in the total cost of 10 I-pads and 5 mobiles.

• A. 10%
• B. 11.14%
• C. 14.63%
• D. 18%

Hint:

Let the mobile's price be a variable, write the I-pad's price as three times that, then compare the total cost before and after the price rise.

Answer 1

The Correct Option is B

Step 1: Set up the variables.
Let the price of one mobile be \(m\).
The price of an I-pad is thrice the price of a mobile, so the price of one I-pad is \(3m\).

Step 2: Find the original total cost.
The original cost of 10 I-pads is \(10 \times 3m = 30m\).
The original cost of 5 mobiles is \(5 \times m = 5m\).
The original cost of everything together is \(30m + 5m = 35m\).

Step 3: Find the new total cost after the price rise.
The I-pad price rises by 10 percent, so the new cost of 10 I-pads is \(30m \times 1.10 = 33m\).
The mobile price rises by 18 percent, so the new cost of 5 mobiles is \(5m \times 1.18 = 5.9m\).
The new total cost is \(33m + 5.9m = 38.9m\).

Step 4: Find the percentage increase.
The increase in cost is \(38.9m - 35m = 3.9m\).
The percentage increase on the original cost is \[ \frac{3.9m}{35m} \times 100 = 11.142857...\% \approx 11.14\% \]

Step 5: Check the other options.
Option (a) 10% would only be true if every device carried the same single price rise, which is not the case here.
Option (d) 18% is just the mobile's own rise and ignores the I-pad entirely.
Option (c) 14.63% does not match this weighted calculation at all.

Final Answer:
The overall cost of 10 I-pads and 5 mobiles rises by about 11.14 percent, so option (b) is correct. \[ \boxed{11.14\%} \]