GATE 2014-EC 8

Question

Industrial consumption of power doubled from $2000 - 2001$ to $2010 - 2011.$ Find the annual rate of increase in percent assuming it to be uniform over the years

• A. $5.6$
• B. $7.2$
• C. $10.0$
• D. $12.2$

Answer 1

we knows total amount owed (A) = P $(1 + \frac{r}{100}) ^{n}$

and it's given that industrial power is doubled from 2000-2001 to 2010-2011.

So, here n=10 and A = 2P

$2P=P(1 + \frac{r}{100}) ^{10}$

$2=(1 + \frac{r}{100}) ^{10}$

$2^{\frac{1}{10}}=(1 + \frac{r}{100})$

$1.07177=(1 + \frac{r}{100})$

$.07177=( \frac{r}{100})$

r=7.17≃7.2

 

Hence,Option (B)7.2 is the correct choice.

Comments

plz tell me how r u finding 2^1/10

even calculator such key not found

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oh! you can find it from calculator. Just type 2^(1/10) and calculator will show you the result.

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To find the value of 2^(1/10) in virtual calculator,

--- open virtual calculator

--- first click 2 and then find the button labelled as X^Y and click it

--- then click .1 or 0.1 (as 1/10 = 0.1 ). u will get the result (1.07177)

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why compound interest, why not simple?

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Try using simple example it is not possible to double amount in ten years using simple interest if r=7.2% but if r is 10% then answer should be c

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because , principle amount is changing every year and we increment on that principle amount hence compound interest