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Updated on: 30 Jul 2017, 20:22
2
13
00:00

Difficulty:

95% (hard)

Question Stats:

52% (03:00) correct 48% (02:49) wrong based on 159 sessions

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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, 07:59.
Last edited by DHAR on 30 Jul 2017, 20:22, edited 2 times in total.
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Joined: 09 Dec 2014
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30 Jul 2017, 09:01
1
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 [ 31.38 KiB | Viewed 3279 times ]

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

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Abhishek....

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Joined: 14 Dec 2015
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30 Jul 2017, 11:15
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

Please name topics properly. Read rule 3 in our RULES OF POSTING. Thank you.
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04 Nov 2018, 08:30
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

VP
Joined: 09 Mar 2016
Posts: 1258

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05 Nov 2018, 10:23
1
1
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 $640 crore per an [#permalink] ### Show Tags 05 Nov 2018, 10:29 1 yashna36 wrote: Hi, I have a doubt..so if we use geometric progression here, n comes to 6 years. where am i going wrong? Company coverage in 2001 has a turn over of 640 cr. In 2003 it will have 5120. Therefore, common ratio (r) is 8 Company Mike in 2001 has a turnover of 40 Cr. In 2001 it will have 160 Cr. Therefore common ratio (r) is 4 Company Coverage, x = 40(4)^(n-1)-----------1 Comany Mike, x = 640(8)^{(n/2)-1}-----------2 Equating 1 and 2, we get n = 6 Can you please help me figure where I am going wrong. Thankyou Hi yashna36 If we look at it from this perspective for Company with 40$ 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.
VP
Joined: 09 Mar 2016
Posts: 1258

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05 Nov 2018, 10:44
1
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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24 Jul 2019, 18:39
Abhishek009 wrote:
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

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

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.
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Re: The turnover of an organization named 'Coverage' was $640 crore per an [#permalink] ### Show Tags 08 Aug 2019, 05:00 Abhishek009 wrote: 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 Answer will be (C) after 8 years... Hi Abhishek, Unable to understand how you got the above figures. Could you elaborate, please? Re: The turnover of an organization named 'Coverage' was$640 crore per an   [#permalink] 08 Aug 2019, 05:00
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