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Directions (1 - 5): Study the following table carefully and answer the questions given below:
Number (N) of Candidates (In lakhs) Appearing for An Entrance Examination from six different States and The percentage (P) of candidates clearing the Same over the years.
STATE → A B C D E F
YEAR ↓ N P N P N P N P N P N P
2004 1.23 42 1.04 51 1.11 32 1.32 24 1.23 36 1.33 31
2005 1.05 43 1.12 62 1.07 47 1.15 49 1.18 55 1.24 24
2006 2.04 38 1.48 32 1.08 28 1.96 35 1.42 49 1.58 26
2007 1.98 41 2.07 43 1.19 30 1.88 46 1.36 47 1.79 29
2008 1.66 53 1.81 50 1.56 42 1.83 60 1.73 57 1.86 34
2009 1.57 39 1.73 36 1.64 52 2.01 56 1.69 55 1.95 37
1
What is the number of candidates not clearing the entrance exam from State A in the year 2007?
Discuss
Answer & Solution
Number of candidates not clearing the exam from state A in 2007
$$\eqalign{ & = \left\{1.98\times\left(100 - 41\right)\%\right\}\text{lakhs} \cr & = \left(1.98\times\frac{59}{100}\right)\text{lakhs} \cr & = \left(\frac{116.82}{100}\times100000\right) \cr & = 116820 \cr} $$
2
What is the average number of candidates appearing for the entrance exam from state D in the years 2007, 2008 and 2009 together?
Discuss
Answer & Solution
Average number of candidates appearing from state D in 2007, 2008, 2009
$$\eqalign{ & = \frac{1.88+1.83+2.01}{3}\text{ lakhs} \cr & = \frac{5.72}{3}\text{ lakhs} \cr & = \frac{5.72\times100000}{3} \cr & = \frac{572000}{3} \cr & = 190666\frac{2}{3} \cr} $$
3
What is the ratio of the total number of candidates clearing the entrance examination from state B in the year 2004 to that of those clearing the entrance examination from State C in the same year?
Discuss
Answer & Solution
$$\eqalign{ & \text{Required ratio} \cr & = \frac{1.04\text{ lakhs}\times51\%}{1.11\text{ lakhs}\times32\%} \cr & = \frac{1.04\times51}{1.11\times32} \cr & = \frac{104\times51}{111\times32} \cr & = \frac{13\times17}{37\times4} \cr & = \frac{221}{148} \cr & = 221:148 \cr} $$
4
What is the total number of candidates clearing the entrance examination from State E and F together in the year 2006?
Discuss
Answer & Solution
Number of candidates clearing the exam from states E and F together in 2006.
$$\eqalign{ & = \left(1.42\text{ lakhs}\times\frac{49}{100}\right)+\left(1.58\text{ lakhs}\times\frac{26}{100}\right) \cr & = \frac{\left(1.42\times49\right)+\left(1.58\times26\right)}{100}\text{ lakhs} \cr & = \frac{69.58+41.08}{100}\text{ lakhs} \cr & = \frac{110.66}{100}\times100000 \cr & = 110660 \cr} $$
5
In which year did the highest number of candidates clear the entrance exam from state D?
Discuss
Answer & Solution
Number of candidates clearing the exam from state D in
$$\eqalign{ & 2008 → \left(1.83\times\frac{60}{100}\right)\text{lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{1.83\times3}{5}\text{ lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{5.49}{5}\text{ lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = 1.10\text{ lakhs} \cr & 2009 → \left(2.01\times\frac{56}{100}\right)\text{lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{2.01\times14}{25}\text{ lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{28.14}{25}\text{ lakhs} \cr & \,\,\,\,\,\,\,\,\,\,\, = 1.12\text{ lakhs} \cr} $$
In rest of the years it is clearly less.
So, it is maximum in the year 2009