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

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The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post Updated on: 30 Jul 2017, 19:22
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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

Originally posted by DHAR on 30 Jul 2017, 06:59.
Last edited by DHAR on 30 Jul 2017, 19:22, edited 2 times in total.
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 30 Jul 2017, 09:04
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DH99 wrote:
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


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
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 30 Jul 2017, 08:01
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DH99 wrote:
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
Attachment:
Capture.JPG
Capture.JPG [ 31.38 KiB | Viewed 2048 times ]

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

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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 30 Jul 2017, 08:42
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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
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 30 Jul 2017, 10:15
DH99 wrote:
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


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The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 04 Nov 2018, 06:08
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
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The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 04 Nov 2018, 07:30
DHAR wrote:
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


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
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The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 05 Nov 2018, 09:03
cherryriya wrote:
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




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 ? :lol:
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 05 Nov 2018, 09:23
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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
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 05 Nov 2018, 09:29
1
yashna36 wrote:
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


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.
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 05 Nov 2018, 09:35
Salsanousi wrote:
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 mashallah :) thank you. i forgot to divide both sides by 40 :) that is why was getting very very wrong answer :lol:
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 05 Nov 2018, 09:44
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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
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Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

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New post 07 Nov 2018, 17:57
DHAR wrote:
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


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
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Re: The turnover of an organization named 'Coverage' was $640 crore per an &nbs [#permalink] 07 Nov 2018, 17:57
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