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The Gross Domestic Product $(GDP)$ in Rupees grew at $7\%$ during $2012-2013$. For international comparison, the $GDP$ is compared in US Dollars $(USD)$ after conversion based on the market exchange rate. During the period $2012-2013$ the exchange rate for the $USD$ increased from $Rs$. $50/ USD$ to $Rs.$$60$/ $USD$. India's GDP in USD during the period $2012-2013$

1. increased by $5 \%$
2. decreased by $13\%$
3. decreased by $20\%$
4. decreased by $11\%$

 GDP before (2012-13) 100 50  = 2 (dollar ) GDP during (2012-13) 107 60    = 1.782(dollar )

now   final value - initial value / initial value

1.783-2/2=   -10.83% (- means decrease  )

In GO Pdf, % symbol is missing at 7
nice:)

Let India's $GDP = Rs. x$

$Rs.\;50=1\;USD$

$Rs.\;x=\dfrac{1}{50}\times x\; USD$

New  $GDP=GDP+0.07\times GDP$

$\quad =Rs\; 1.07x$

$Rs\; 60=1\; USD$

$Rs\; 1.07x=\dfrac{1}{60}\times 1.07x$

$\text{Change in GDP} = \dfrac{new-old}{old}\times 100$

$\quad =\dfrac{\left(\dfrac{1.07x}{60}\right)-\left(\dfrac{x}{50}\right)}{\dfrac{x}{50}}\times 100$

$\quad =\dfrac{\left(\dfrac{-13x}{6000}\right)}{\left(\dfrac{x}{50}\right)}\times 100$

$\quad = \left(\dfrac{-13}{120}\right)\times 100$

$\quad = -0.10833 \times 100$

$\quad = -10.833$

$\quad \approx -11$

So, there is an $11\%$ decrease

D)
In such questions take "What we have to find" as $100$ (easy way). i.e Let India's GDP be Rs $100.$
When GDP was Rs 100 exchange rate was $Rs 50\;USD$

$1\; USD = Rs\; 50$
then $? = Rs\; 100$

$Rs\; 100 =\dfrac{100}{50}$ Dollars

GDP grew by $7 \% = 100+7 \%(100)=100+7= Rs\; 107$
When GDP is $Rs\; 107$ exchange rate is $Rs\; 60\;USD$

$1\; USD = Rs\; 60$
then $?= Rs\; 107$
$Rs \;107 =\dfrac{107}{60}$ Dollars

$\dfrac{\left(\dfrac{107}{60}\right)}{\left(\dfrac{100}{50}\right)}\times 100 = 89 \%$ increase of $USD.$

which means Indian GDP has decreased , and it has decreased to $(100-89) = 11 \%$

1 comment

((107/60)/(100/50))*100=89%