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

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

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

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

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 ?

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

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.

Salsanousi mashallah thank you. i forgot to divide both sides by 40 that is why was getting very very wrong 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

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

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.

Hi Abhishek,

Unable to understand how you got the above figures. Could you elaborate, please?

what is the actual calculation for "coverage" ?

640(1+7/2)^2t

or

640(1+7)^t/2



please explain !!!!!

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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