Government of Tamil Nadu conducted a Trade Fair in Island grounds, Chennai from 3rd January to 31st January 2012. The Fair attracted stalls from different business activities such as banking, BPO, software companies, educational institutions, furniture makers, luxury goods dealers etc. The fair also had a drama festival conducted every day. Surprisingly the trend observed in the number of spectators for the drama was following a trend. On the first day 120 people attended. On the second day it had only 80 people i.e. number was less by 40. On the third day again the number increased by 120 from the previous day and on the fourth day the number came down by 40 from the third day figure. Assuming this trend continued on which day the drama would have had full capacity of auditorium -1080 seats?

a) 25th January b) 23rd January c) 27th January d) none of these.

Answer : c) 27th January.

Solution :

Total capacity of the drama auditorium –1080

As per statements in question the number of people on first few days are as follows :

First day : 120.

Second day : 80.

Third day : previous day’s strength + 120 = 80 + 120 = 200.

Fourth day : previous day’s strength – 40 = 200 – 40 =160.

Fifth day : previous day’s strength + 120 = 160 + 120 = 280

Sixth day : previous day’s strength – 40 = 240 – 40 = 240.

You can now note a trend that for every two days the strength effectively increases by 80.

So in 24 days the number of spectators will be 80 x 12 = 960.

On the 25th day 960 + 120 = 1080.

The full capacity will be reached on 25th day from start of fair. Since the start date is 3rd January, the capacity will be reached on 27th January.

Question 2

Marco Polo, the adventurous traveler was travelling through the thick forests of Assam. It was quite dark and he had problem in wading through the forest. Suddenly he fell inside an unwalled well of 130 metre depth. He struggled to climb up to get on to the level ground and escape. But unfortunately he found it difficult. He was climbing up 10 metres in the first hour whereas in the next hour he was getting dropped by four metres on account of slippery surface . This process continued viz. in the first hour he was climbing up 10 metres and in the next hour he was slipping down by 4 metres. How many hours he would have taken to climb to top of well?

a) 21 hours b) 20 hours c)41 hours d) none of these.

Answer : c) 41 hours.

Solution :

In the first hour he climbs 10 metres

In the second hour he slips down – 4 metres

So in 2 hours he climbs up 10 – 4 = 6 metres

hours metres

2 6

40 ?

In 40 hours he will climb up 40 x 6 / 2 = 120 metres. Since the depth of the well is 130 metres, in 41st hour he will climb another 10 metres and would had reached the top of well (before falling down by 4 metres again). So in 41 hours he climb up 10 metres and reach the top of the well.

Question 3

Mr.King Kong an European aged 52 years was suffering from various ailments such as high blood pressure, blood sugar, cholesterol. He was 5 feet 6 inches tall. Optimal weight for his height is 130 pounds. On 10th January 2012 he found his weight was 223 pounds. The doctors advised him to adopt weight planning. They prescribed exercises, food etc. On the first day he found he was able to reduce his weight by 8 pounds. He felt very happy. But he found that on the next day his weight increased by 3 pounds. He continued to perform exercises. On which date he would have been able to reduce his weight to optimal weight.

a) 14th February 2012 b) 15th February 2012 c) 25th February 2012 d) none of these.

Answer : a) 14th February 2012.

Solution :

Present weight – 223 pounds

Optimal weight – 130 pounds

Weight to be reduced – 223 – 130 = 93 pounds

Every two days his weight comes down by 5 pounds. (8-3 = 5 )

In 34 days his weight will be reduced by 85 pounds. And on 35th day he will be able to reduce his weight by 93 pounds to 130 pounds.

35th day from 10th January 2012 -14th February 2012.

Question 4

A group of students from Netherlands visited Chennai to study about the various aspects of life prevalent in Chennai. They also studied about the weather forecasts. The average temperature of days from Sunday to Wednesday was 36 degrees and that of from Monday to Thursday was 33.5 degrees, The temperature on Thursday was 2/3 of Sunday. What was the temperature on Sunday?

a) 20 b) 30 c) 40 d) 38

Answer : b) 30 degrees

Solution :

Average Temperature from Sunday to Wednesday – 36.

Total temperature from Sunday to Wednesday – 36 x 4 = 144 deg.

Average temperature from Monday to Thursday – 33.5 deg.

Total temperature from Monday to Thursday – 33.5 x 4 = 134

If the total temperature from Monday to Wednesday be K

Then, Sunday’s temperature + K = 144 -> eq 1

Thursday’s temperature + K = 134 -> eq 2

It is stated that Thursday temperature was 2/3 of Sunday. Applying this to eq 2, we get :

2/3 (Sunday’s Temperature) + K = 134 -> eq 3

Eq 1 – Eq 3 => 1/3 (Sunday’s Temperature) = 10. Therefore, Sunday temperature = 30 deg.

Question 5

A prominent School in Chennai had classes from LKG to XII standard. A study was made about the marks scored by students of XII in a government examination. The average marks of 60 students in a class was 45. The average marks of the boys in the class is 40 and the average marks of the girls in the class is 50. What is the ratio between the number of boys and girls in the class?

a) 1: 1 b) 2 : 1 c) 3 : 1 d) none of these.

Answer : a) 1 : 1

Solution :

Total marks of 60 students = 60 x 45 = 2700

Suppose number of girls = x

Number of boys = (60 – x)

Number of girls X average marks of girls + Number of boys x average marks of boys = 2700

x X 50 + (60 – x) 40 = 2700

50x + 2400 – 40x = 2700

By simplifying we get x = 30. Number of boys = 30 . Number of girls = 60 – x = 60 – 30 = 30

Therefore ratio of number of boys to girls = 30 / 30 = 1

Question 6

The average number of visitors to a museum from Wednesday to Saturday was 2345. Average number of visitors to it from Thursday to next Sunday was 2100. If the number of visitors to the museum on Sunday was 1820, find the number of visitors to the museum on Wednesday.

a) 2700 b) 2900 c) 2400 d) 2800

Answer : d) 2800.

Solution :

The average no. of of visitors from Wednesday to Saturday – 2345

Total number of visitors from Wednesday to Saturday – 2345 x 4 = 9380

Average number of visitors from Thursday to Sunday – 2100

Total number of visitors from Thursday to Sunday – 2100 x 4 = 8400

Number of visitors on Sunday – 1820.

So number of visitors from Thursday to Saturday – 8400 – 1820 = 6580

But it is given that, Number of visitors from Wednesday to Saturday – 9380

Therefore, Number of visitors on Wednesday = 9380 – 6580 = 2800

Question 7

A prominent School at Siliguri had three batches of students numbering 35,40 and 50 respectively. The average marks of these batches is 40, 45 and 55 respectively. What is the average mark of all the three batches students put together?

a) 48.6 b) 49.6 c) 51 d) 47.6

Answer : d) 47.6

Solution :

Total marks of all 3 batches = Number of students in I batch x Average of I batch + Number of students in II batch x Average of I batch + Number of students in I batch x Average of I batch = [ (35 x 40) + (40 x 45) + (50 x 55)]

Total number of students in all III batches = 35 + 40 + 50 = 125

Average marks of all students of III batches = Total marks of all 3 batches / Total number of students.

= [ (35 x 40) + (40 x 45) + (50 x 55)] divided by 125 = 47.6