SOLUTION: In the course of a year 1/3 of a company's capital increase by 4%.1/5 of it decreases by 5% and the rest increases by 10%.what is the percentage increase on the whole???

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In the course of a year 1/3 of a company's capital increase by 4%.1/5 of it decreases by 5% and the rest increases by 10%.what is the percentage increase on the whole???      Log On


   

Question 1122764: In the course of a year 1/3 of a company's capital increase by 4%.1/5 of it decreases by 5% and the rest increases by 10%.what is the percentage increase on the whole???
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1/3 * 4 - 1/5 * 5 + (1 - 1/3 - 1/5) * 10 = 5% overall increase.

1 - 1/3 - 1/5 = 1 - 5/15 - 3/15 = 1 - 8/15 = 7/15

1/3 * 4 - 1/5 * 5 + 7/15 * 10 = 5%

5/15 * 4 - 3/15 * 5 + 7/15 * 10 = 20/15 - 15/15 + 70/15 = 75/15 = 5%

1/3 * 1.04 + 1/5 * .95 + 7/15 * 1.10 = 1.05 - 1 = .05 * 100 = 5%.

it all points to a 5% overall increase.

for example:

assume the original capital is 15000.

1/3 of that increases by 4%
1/5 of that decreases by 5%
7/15 of that increases by 10%.

that means that .....

5000 increases by 4% = 5000 * 1.04 = 5200
3000 decreases by 5% = 3000 - .05 * 3000 = 2850
7000 increases by 10% = 7000 * 1.10 = 7700.

total increase is 5200 + 2850 + 7700 - 15000 = 15750 - 15000 = 750.

750 / 15000 = .05 * 100 = 5%.

note that 3000 - .05 * 3000 = 3000 * (1 - .05) = 3000 * .95 = 2850

your solution is that the overall increase is 5%.