GATE CSE 2014 | Set 3 | GA | Question: 8

Question

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 $2012-2013$

• A. increased by $5 \%$
• B. decreased by $13\%$
• C. decreased by $20\%$
• D. decreased by $11\%$

Comments

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  )

 

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In GO Pdf, % symbol is missing at 7

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nice:)

Answer 1

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

Answer = option D

Answer 2

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 $(100-89) = 11 \%$

Comments

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

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@Srinath Jayachandran

$\dfrac{\Big(\dfrac{107}{60}\Big)}{\Big(\dfrac{100}{50}\Big)} \times 100\% = 89.16\% \approx 89\%$

this does not represents $89\%$ increase in $USD$ but it represents that the current value of $GDP$ in $USD$ has become $89\%$ of the original value. in simpler terms it means that if in $2012$, $GDP=\$100$ then $GDP=\$89$ in $2013$.

Answer 3

Simple

First take gdp 100

2012---- gdp = 100

Usd = 50 so

100/50=2

Then 2013 gdp increase 7 %

New gdp 107

2013 usd increased 60

107/60=1.78333.

% increase or decrease = old - new / old

0.2167 /1.7833= 0.99...

0.999*100 = round of 11 %

 

Answer 4

\begin{array}{|l|c|c|c|}
\hline
 & \textbf{GDP grew to} & \textbf{Rupee weakened to} & \textbf{Real "dollar worth"} \\
\hline
\text{Before} & 100 & 100 & 1 \text{ (starting point)} \\
\hline
\text{After} & 107 & 120 & \dfrac{107}{120} \approx 0.89 \\
\hline
\textbf{Change} & \textbf{+7\%} & \textbf{+20\%} & \dfrac{0.89 - 1}{1} \approx -10.83\% \approx \textbf{11\% decrease} \\
\hline
\end{array}