Question

The cost of manufacturing a car depends upon three items: cost of material, labour and overheads. In a year, the cost of these items were in the ratio 4:3:2. Next year the cost of material increased by 10%, cost of labour increased by 8% but cost of overheads reduced by 5%. If same number of cars were produced in each year, then the percentage increase in the price of the car, would be:

• A. 6%
• B. 7%
• C. 9%
• D. 10%

Answer 1

The Correct Option is A

Concept:

• When three components of a cost are given in a ratio, take the ratio numbers directly as the parts of the total cost.
• Apply each item's own percentage change only to its own part.
• Overall % change = (New total - Old total)/(Old total) x 100.

Step 1: Set up the parts from the given ratio
Material : Labour : Overheads = 4 : 3 : 2. Take these as 4, 3, 2 units, so old total cost = 4 + 3 + 2 = 9 units.

Step 2: Apply the percentage change to each part
Material: 4 x 1.10 = 4.4
Labour: 3 x 1.08 = 3.24
Overheads: 2 x 0.95 = 1.90

Step 3: Find the new total cost
New total = 4.4 + 3.24 + 1.90 = 9.54 units.

Step 4: Find the percentage increase
Increase = 9.54 - 9 = 0.54
% increase = (0.54/9) x 100 = 6%

Final Answer: 6%