Aptitude

Question

A country's GDP grew by $7.8\%$ within a period. During the same period the country's per-capita-GDP (= ratio of GDP to the total population) increased by $10\%$. During this period, the total population of the country

1. increased by $4\%$
2. decreased by $4\%$
3. increased by $2\%$
4. decreased by $2\%$

Comments

• Let the inital GDP be $x$ and total population be $y$.
• After period GDP becomes $1.078x$
• Initially Per capita GDP$=\Large\frac{x}{y}$
• After period Per capita GDP becomes $=1.1\times \frac{x}{y}$
• Population after Period $=\Large\frac{1.078x\times y}{1.1x}$ $=0.98y=\text{2% less}$

Answer d) : $\text{decreased by 2%}$

Answer 1

Ans (D)

Let's say initially GDP = 1000 and Population P = 100

So, its initial per capita would be Pc = GDP/P = 10.

Now GDP grew by 7.8% => new GDP = 1078

Let's say new population is 'X'

New Per-capita increased by 10% => new Pc = 11.

So, new Pc = $\frac{new GDP}{new Population}$

11 =$\frac{1078}{X}$ => X=98

So, Population decreased from 100 to 98 => Ans (D)