Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
The cost of manufacturing a car is made up of three items : cost of materials, labour and overheads. In a year, the cost of these items were in the ratio 4 : 3 : 2. Next year the cost of materials rose by 10%, cost of labour increased by 8% but the overheads reduced by 5%. Find the increase percent in the price of the car.
Answer
Answer (as printed):
Explanation
Let the cost of materials, labour and overheads in the first year be ₹$4x$, ₹$3x$ and ₹$2x$ respectively. Then, cost of materials in second year $=110\%$ of ₹$4x=₹\left(\frac{110}{100}\times 4x\right)=₹\frac{440x}{100}$. Cost of labour in second year $=108\%$ of ₹$3x=₹\frac{324x}{100}$. Overheads in second year $=95\%$ of ₹$2x=₹\frac{190x}{100}$. Price of the car in first year $=₹(4x+3x+2x)=₹9x$. Price of the car in second year $=₹\left(\frac{440x}{100}+\frac{324x}{100}+\frac{190x}{100}\right)=₹\frac{954x}{100}$. Increase in price $=₹\left(\frac{954x}{100}-9x\right)=₹\frac{54x}{100}$. $$\therefore \quad \text{Increase \%}=\left(\frac{54x}{100}\times\frac{1}{9x}\times 100\right)\%=6\%.$$
Explanation as extracted from the printed page; notation may be imperfect.