a) The cost of manufacturing a car is made up of three items : cost of material, labour, overheads. In a year, the cost of these items were in the ratio 4:3:2. Next year the cost of material rose by 10%, cost of labour increased by 8% but the overheads reduced by 5%. Find the increase percentage in the price of the car.
Answers
Answer:
before increase total cost = 4+3+2=9,
after increasing the cost = 9.54
so increase of .54 over 9 , equal to 6%
The increase percentage in the price of the car is 6%.
Given:
The cost of manufacturing a car is made up of three items : cost of material, labour, overheads. In a year, the cost of these items were in the ratio 4:3:2. Next year the cost of material rose by 10%, cost of labour increased by 8% but the overheads reduced by 5%.
To find:
Find the increase percentage in the price of the car.
Solution:
Let the cost of the car be Rs. x
Then,
sum of ratio = 4 +3+2 = 9
Material costs = ratio of material/ sum of ratio * total cost of car = 4/5 * 9
Similarly,
Labour costs = 3x/9
Overhead costs = 2x/9
New material costs = Original cost + 10% of original cost = 4x/9 + 10% of 4x/9
= 4x/9 + 10/100 * 4x/9 = 4x/9 + 4x/90
= (40x + 4x)/90
= 44x/90
New labour costs = Original cost + 8% of original cost = 3x/9 + 8% of 3x/9
= 1x/3 + 8/100 * 1x/3 = x/3 + 8x/300
= (100x + 8x) / 300
= 108x/300 = 36x/100
New overhead costs = Original cost - 5% of original cost = 2x/9 - 5% of 2x/9
= 2x/9 - 5/100 * 2x/9 = 2x/9 - 10x/900
= 2x/9 - x/90
= (20x - x) / 90
=19x/90
Increase in the cost of T.V. = New cost - original cost of each cost
= (44x/90 - 4x/9) + (36x/100 - 3x/9) + (19x/90 - 2x/9)
= 4x/90 + 2x/75 - x/90 [because cost of overheads were reduced]
= (20x+12x-5x)/450
= 27x/450 = 3x/50
∴Increase in cost= increase in cost/original cost * 100
= (3x/50)/x * 100
x will be canceled as numerator and denominator
= 3/50 * 100
= 3 * 2 = 6%
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