Twenty years ago, the population of Bedford was 40% less tha

Question

Twenty years ago, the population of Bedford was 40% less than that of Tecumseh. The population of Bedford has since tripled and is now just 10% less than Tecumseh’s. By what percent has the total population of the two towns increased over the past 20 years?

A. 100%
B. 120%
C. 137 1/2 %
D. 160%
E. 175%

A. 100%
B. 120%
C. 137 1/2 %
D. 160%
E. 175%

GridLock · Answer

Twenty years ago 
Let the population of Tecumseh = T
Therefore, the population of Bedford = 0.6T

Getting rid of the decimals for a better variable setup by multiplying by 5 and substituting T' as a new variable that represents T/5
(I have continued to use T instead of T' in each place for easier writing)

=> Population of Tecumseh = 5T
=> Population of Bedford = 3T
Total population = 8T

Today 
Population of Bedford = 3 * (Old Population) = 3 * 3T = 9T
Let the New Population of Tecumseh = N
We know that Bedford's current population is 10% less than Tecumseh
=> 0.9N=9T
=> N= 10T

Total population today = 9T+10T = 19T

Increase in population 
=   * 100
=  *100 = 137.5%

Therefore C is the answer

findingmyself · Answer

The mistake I made initially was to consider population and age to have the same kind of problem solving method.

Twenty years ago, the population of Bedford was 40% less than that of Tecumseh. The population of Bedford has since tripled and is now just 10% less than Tecumseh’s. By what percent has the total population of the two towns increased over the past 20 years?

A. 100%
B. 120%
C. 137 1/2 %
D. 160%
E. 175%

Pop T= X
Pop B= 0.6X

B now is 1.8X
T now is N
1.8X= 0.9N
N= 2X

Hence T now is 2X

Total Inc= 3.8X-1.6X/1.6X= 2.2/1.6= 1.375 in % it will be 137.5%

kevincan · Answer

....................... Bedford ....... Tecu

20 years ago.........6..................10
Now .....................6*3..............y

18= 0.9y
Y=20

So we need to compare 38 with 16

38:16 = 19: 8= 2.375 : 1

suntprovident · Answer

There's a much easier way to solve these questions using actual numbers since we just need to find the fraction/ percent change.

Assume the population of Town T to be 100 Twenty Years ago. We are told

1. that the population of Town B is 40% less Twenty years so population of Town B twenty years ago = 60 and total population is 100+60 twenty years ago

2. Since then the population of Town B has tripled. Ok so twenty years ago it was 60, now it triples so population increases to 180

3. The population of Town T is now only 10% less than Town B. Key trap is to understand that the base is Town B i.e. 90% of Town B = 180 and not 110% of Town T = Town B. Hence we get Town B as 200

4. Adding the two we get total population as 380

5. We need the percent change - (380-160)/160*100

6.Option C

Twenty years ago, the population of Bedford was 40% less tha

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Twenty years ago, the population of Bedford was 40% less tha

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