The turnover of an organization named 'Coverage' was $640 crore per an

Question

The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years

Ramyanag · Accepted Answer

Let x be the number of years after which turnovers of both the firms be equal. 
For 'Miles' increase by 300% every year==> (100+300)/100 = 400/100 ==> 4 times every year
For 'Coverage' increase by 700% every two years ==> (100+700)/100 ==> 800/100 ==> 8 times every two years
We can write the equation by the given data as:

40*4^x=640*8^{x/2}  (as for 'Coverage' the rise is every two years)
 4^x=16*8^{x/2}  ==>  2^{2x}=2^4*(2^3)^{x/2} 
 2^{2x}=2^{(8+3x)/2}  ==> 4x=8+3x ==> x=8 
Answer: C

cherryriya · Answer

Apply the compound interest to solve it quickly. Assume that the turnover of both the companies becomes same at the end of "t" years.

for the organization named "Coverage" , the turnover in t years will be = 640 * ((1 + 7) ^ t/2)
 (its t/2 because the turnover increases every 2 years)

for the organization named "Miles", the turnover in t years will be = 40 * ((1 + 3) ^ t)

The coverage will be same after "t" years, hence: 
 640 * ((1 + 7) ^ t/2) = 40 * ((1 + 3) ^ t)

Solve for "t" , and you will get t = 8 years

Abhishek009 · Answer

Capture.JPG Answer will be (C) after 8 years...

yashna36 · Answer

Hi,

I have a doubt..so if we use geometric progression here, n comes to 6 years. where am i going wrong?
Company coverage in 2001 has a turn over of 640 cr. In 2003 it will have 5120. Therefore, common ratio (r) is 8
Company Mike in 2001 has a turnover of 40 Cr. In 2001 it will have 160 Cr. Therefore common ratio (r) is 4

Company Coverage, x = 40(4)^(n-1)-----------1
Comany Mike, x = 640(8)^{(n/2)-1}-----------2

Equating 1 and 2, we get n = 6
Can you please help me figure where I am going wrong. Thankyou

dave13 · Answer

pushpitkc chetan2u , Gladiator59 hello there! formula for compound interest A = p(1+\frac{r}{n})^{nt} p - principal/ amount r - annual rate of interest t - number of years the amount is deposted n - number of years the interest is compounded a - money accumulated after n years 640(1+\frac{7}{2})^{2t} = 40(1+\frac{3}{1})^t 640(1+3.5)^{2t} = 40(1+3)^t 640(4.5)^{2t} = 40(4)^t 2880^{2t} = 160^t now what to do ?

i got stuck here

for more information about compound formula click here

https://qrc.depaul.edu/StudyGuide2009/N ... terest.htm

dave13 · Answer

can anyone solve for T after this 640 * ((1 + 7) ^ t/2) = 40 * ((1 + 3) ^ t)? need detailed algebraic solution Bunuel will you be my hero today ?

Salsanousi · Answer

Hi  dave13

640 * (1+7)^t/2 = 640 * (8)^t/2 = 640 * (2^3)^t/2 = 640 * 2^(3t/2)

The other hand is 40 * 4^t = 40 * 2^2t

Let 40 * 2^2t = 640 * 2^(3t/2) divide by 40 on both sides.

2^2t = 16 * 2^(3t/2)

2^2t = 2^4 * 2^(3t/2) Since all the base is equal we can equate the powers.

2t = 4 + 3t/2

0.5t = 4

t = 8

Hope this helps :D

Salsanousi · Answer

Hi  yashna36

If we look at it from this perspective for Company with 40$ per annum the increase is 300% per year correct?

so it is 40 * (1 + 300%) = 40 * (1+3) = 40 * 4 (per year)

So every year it will increase by 4. This way 40*4 for first year and 40*4*4 for 2nd year etc.. which can be replaced by the compound interest equation.

where 40 is the principal amount 40* (1+3)^x because it goes per year.

The other equation is 640 * (1+7)^(x/2) the reason we are dividing by 2 is because the increase happens every 2 years.

I hope this helps.

dave13 · Answer

Salsanousi mashallah

thank you. i forgot to divide both sides by 40

that is why was getting very very wrong answer

Salsanousi · Answer

I tried approaching the question with backsolving

I tried with 6 first so 40 * 4^6 = 40 * 2^12 and tried to make it equal to the other side of 640 * 8^3 (because every 2 years it happens)

40 * 2^12 = 640 * 2^9

2^12 = 16 * 2^9

2^12 = 2^4 * 2^9 which is not true. 2^12 < 2^13

I tried with C

40 * 4^8 = 640 * 8^4

2^16 = 2^4 * 2^12

2^16 = 2^16

ScottTargetTestPrep · Answer

For Miles, when the turnover increased by 300% each year, it means that there was a fourfold increase per year. Let n be a positive integer. In 2n years (after 2001), Miles’ turnover is 40 x 4^(2n). For Coverage, when the turnover increased by 700% every two years, it means that there was an eightfold increase every two years, and so Coverage’s turnover is 640 x 8^n. Since we are interested in determining the number of years since 2001 it took for their turnovers to be the same, we equate the two growth expressions in the following equation:

40 x 4^(2n) = 640 x 8^n

40 x 16^n = 640 x 8^n

16^n/8^n = 640/40

2^n = 16

n = 4

Therefore, in 2 x 4 = 8 years, the two turnovers will be the same.

Answer: C

Harsh2111s · Answer

Year-Coverage-Miles
2001-640-40
2002-640-160
2003-5120-640
2004-5120-2560
2005-40960-10240
2006-40960-40960

I am getting same value in 6th year itself.
Coverage growth is once in 2 years while miles have every year.
Coverage will be 8 times in every 2 years while miles would be 4 times from previous year.

Need to what I am doing wrong.

Fdambro294 · Answer

Notice that all the Answer Choices are in increments of 2 years. This means that the turnover for each must equate after a year when Coverage increases by 700%

Concept 1: an Increase by 700%—-> same as 8 * Times the Original Number.

Similarly, and Increase by 300% ——> same as 4 * Times the OriginL Number.

Concept 2: successive percentage changes can be applied in a row without regard to order

Thus, an Increase in Miles by 300 % at the end of year 1 and then an Increase in Miles by 300% at the end of year 2 is equivalent to:

4 * ( 4 * ($40 mill) ) = (16) * (40 mill)

Let Exponent N = the count of every TWO-2 Years that passes

After how many 2 year increments will the Turnover become equal?

Coverage every 2 years:

(8)^N * (Original Amount of $640)

Miles every 2 years:

(16)^N * (Original Amount of $40)

Setting up the Equation:

(8)^N * (640) = (16)^N * (40)

(8)^N / (16)^N = (40) / (640)

——taking the Exponent N as Common——

(8 / 16)^N = 40 / 640

——simplifying fractions——

(1 / 2)^N = 1 / 16

N = the 4th Power

Thus, after 4 - TWO Year increments the turnovers in each company will be equal

4 * 2 = 8 years

-C-

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