In the production of fans three types of costs are involved. Cost of raw material, expenditure on labour and miscellaneous costs. Ratio of expenditure on these cost in one year is 4 : 3 : 3. In the next year cost of raw material increased by 10%, expenditure on labour increased by 6% and miscellaneous expenditure decreased by 5%. Find the percentage rise in the cost of fan.
1). 6.3%
2). 8.1%
3). 4.3%
4). 4%
Three types of cost are cost on raw material, labour cost and miscellaneous cost
Ratio of expenditure on these cost is 4 : 3 : 3
Let the cost of the raw material be 4x.
Then increase in cost of raw material = 10% of 4x = 0.4x
Let the expenditure on the labour be 3x
Then increase in expenditure on the labour = 6% of 3x = 0.18x
Let the expenditure on the miscellaneous cost be 3x
Then decrease in miscellaneous cost be = 5% of 3x = 0.15x
Total increase in expenditure = 0.4x + 0.18x – 0.15x = 0.43x
Now, the percentage rise $(= \;\frac{{0.43x}}{{10x}} \times 100 = 4.3)$
Thus, the percentage rise in the cost of fan is 4.3%