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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.

1. $5.6$
2. $7.2$
3. $10.0$
4. $12.2$

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+1
n=10 how?  when subtracting 2000 from 2011 will give n as 11.

Here we need to consider compound interest
consumption is doubled in $10$ years

$2P = P \left [ 1+ \frac{R}{100} \right ]^{10}$

$2= \left [ 1+ \frac{R}{100} \right ]^{10}$

$\sqrt[10]{2} \times 100=100+R$

$1.07177 \times 100 = 100 +R$

$R=7.177 \approx 7.2$

So, ans is option B

by Boss (11.6k points)
edited
0
why compound interest, why not simple?
+1
Hello kiran

where did you read simple/compound interest in question?

What he wrote is general formula for series of increments in %

if some quantity $P$ increases $x$% then it will become $P (1+\frac{x}{100})$ , now if it again increases $y$% then it will overall $P(1+\frac{x}{100})(1+\frac{y}{100})$.

in general sense if P increases $n$ times with $x$% each time then final value of $P$ will be $P(1+\frac{x}{100})^n$
0

Find the annual rate of increase in percent assuming it to be uniform over the years.

If principal amount is X and Rate of interest is 20% then,

 Amount after 1 year 2 years 3 years Compound Interest 1.2X 1.44X 1.728X Simple Interest 1.2X 1.4X 1.6X

 Increase in 0th year to 1st year Increase in 1st to 2nd year Increase in 2nd to 3rd year Compound Interest 1.2X-X=0.2X 1.44X-1.2X=0.24X 1.728X-1.4X=0.328X Simple Interest 1.2X-X=0.2X 1.4X-1.2X=0.2X 1.6X-1.4X=0.2X

Compound interest doesn't seem to give uniform rise over the period :/

0

what should be the write answer then?

I m not getting why B..why not C?

As compound interest not increases uniformly?

0
Because, you seems to be not considering the point that it's not "amount of power consumption increase in a year" that is constant. The quantity that is constant is "percentage increase of power consumption during a year relative to previous year".
+1 vote
Total price = X rs.

X rs. in 10 years rate of interest rs.X

1 rs.  "    10  "       "    "    "       rs X/X=1

1 rs.  "      1  "      "    "    "        rs. 1/10⨉100=10

Ans will be (C)
by Veteran (119k points)

difference value = increased value - original value

rate of increase = $\left ( \frac{difference value}{original value} \right )100$

here if original consumption value = x

increased consumption value = 2x

difference value = 2x-x = x

so rate of increase = $\left ( \frac{x}{x} \right )100$ = 100%

but it is over span of 10 years. so annual rate of increase is 100/10 =10.0 (as increase is uniform over years)

by Active (3.6k points)
0
@sheshang if yo feel that this explation is wrong please cross it otherwise someone upvote it

and hence it create the confusion to new user which one is right answer (whether this one or best one)