A. 1530 m
B. 1680 m
C. 1750 m
D. 3600 m

Answer: Option B

Explanation:
We know that, Time =\(\frac {Distance}{Speed}\)

Speed = 60m/min = \(\frac {60}{60}\) m/sec = 1 m/sec
We know that,
Time along the park (circumference) – Time along the diameter = 60 minutes
∴\(\frac {2πr}{1}\) – \(\frac {2r}{1}\) = 60 minutes

∴ 2r (\(\frac {22}{7}\)– 1) = 3600 seconds

∴ r = 840m
∴ Diameter = 2 x radius = 1680m.

2. Working alone Pramod takes complete April to build pavement. His friend Kishan is 25% faster than him at the same work. Working alone, how many days will Kishan take to build the same pavement?

A. 20 days
B. 24 days
C. 22.5 days
D. 37.5 days

Answer: Option B

Explanation:
April has 30 days. So Pramod takes 30 days to build the pavement.
Kishan is 25% faster than Pramod
25% =\(\frac {25}{100}\) = 0.25

This means, if Pramod is 1, then Kishan is (1+0.25) = 1.25
Pramod takes 30 days to do the work.
Kishan will take = \(\frac {30}{1.25}\)= 24 days to get the work done.

3. An 80L solution of alcohol and water has 45% alcohol in it. If you want the mixture to be 75% alcohol, how much alcohol would you add to it?

A. 30 litres
B. 75 litres
C. 96 litres
D. 110 litres

Answer: Option C

Explanation:
Current alcohol quantity =\(\frac {45}{100}\)x 80 = 36 Litres

Let A be alcohol added.
So, 36 + A =\(\frac {75}{100}\) x (80+A)

∴ A = 96 Litres = This is the additional quantity of alcohol to be added.

4. The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q?

A. 2008
B. 2009
C. 2010
D. 2011

Answer: Option D

Explanation:
Let the commodity P costs 40 paise more than the commodity Q after n years.

Price of the commodity P in 2001 = Rs.4.20

Since the price of the commodity P increases by Rs 0.40 every year,
Price of the commodity P after n years from 2001 = Rs.4.20 + (n × .40)

Price of the commodity Q in 2001 = Rs.6.30

Since the price of the commodity Q increases by Rs 0.15 every year,
price of the commodity Q after n years from 2001 = Rs.6.30 + (n × .15)

Since the commodity P costs Rs. 0.40 more that the commodity Q after n years from 2001,
4.20 + (n × .40) = 6.30 + (n × .15) + 0.40
=> (40n – .15n) = 6.30 – 4.20 + 0.40 = 2.5
=> .25n = 2.5
=> n = \(\frac {2.5}{.25}\) = \(\frac {250}{25}\) = 10
=> Commodity P costs Rs.0.40 more that the commodity Q after 10 years from 2001.
i.e., in 2011.

5. Prithvi rolled a dice twice and he saw that the addition of two numbers that appeared on the top face was 8. Find the probability of getting a 4 on the top face of the dice in the first throw.

A. \(\frac {1}{36}\)
B. \(\frac {2}{36}\)
C. \(\frac {1}{6}\)
D. \(\frac {1}{5}\)

Answer: Option A

Explanation:

A dice has 6 faces.
So there are 6 possible outcomes
Dice is rolled once AND then again.
So total possibilities = 6 x 6 = 36

The sum should be 8 of the 2 throws.
So which combination of numbers from 1 to 6 will yield us a sum of 8?
They are – (2,6); (6,2); (3,5); (5,3); (4,4)

So there are total 5 possibilities where addition is 8.
But only 1 possibility where first throw of dice is 4.
So, Probability for the first throw to be 4 and sum to be 8 = \(\frac {1}{36}\)

A. 110
B. 110.5
C. 120
D. 220

Answer: Option C

Explanation:
Average of ‘n’ multiples of any number = Number x \(\frac {(n+1)}{2}\)

IMPORTANT NOTE –
It is similar to the average of first n natural numbers.
Just multiply by the number as shown above.

Here n = 19

Average of 19 multiples of 12 = 12 x \(\frac {(19+1)}{2}\)= 120

2. A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?

A. 6.25
B. 25
C. 50
D. 12.5

Answer: Option B

Explanation:
Dividend on 1 share = \(\frac { (12.5 * 50)}{100}\) = Rs.6.25
Rs.25 is income on an investment of Rs.100
Rs.6.25 is income on an investment of Rs. \(\frac {(6.25 * 100)}{25}\) = Rs.25

3. Rajesh was shifting his shop. When he tried to pack 85 similar cartons in each bag, he realized that he could not completely fill 9 bags. However, when he reduced the number of cartons in each bag to 58, 13 bags got insufficient. However, in the end, he could pack all the cartons by packing X carton in X bags. How many total cartons did he have?

A. 729
B. 765
C. 784
D. 812

Answer: Option

Explanation:
Since X bags are there and each has X cartons, Total cartons = X * X = X\(^{2}\)
Only options C and D are perfect squares.
729 is a perfect square
But it cannot be answered as the condition is that with 58 books in each bag, 13 bags are not sufficient.
58 x 13 = 754 > 729
So if 729 is the answer, 13 bags are sufficient.
So answer is Option D = 784.

4. The ages of 10 students and their teacher are such that the average of first 7 student’s age is 15 years; average of last three student’s age is 11 years. The average age of all the students and their teacher together is 15 years. Find the age of the teacher.

A. 24 years
B. 27 years
C. 30 years
D. 33 years

Answer: Option B

Explanation:
Total age of 10 students and their teacher = 11 x 15 = 165 years.

Total age of first 7 students = 7 x 15 = 105 years

Total age of 3 students = 3 x 11 = 33 years

∴ Total age of 10 students = 105 + 33 = 138 years

Age of their teacher = 165 – 138 = 27 years.

5. The least perfect square, which is divisible by each of 21, 36 and 66 is:

A. 213444
B. 214344
C. 214434
D. 231444

Answer: Option A

Explanation:

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 2\(^{2}\) x 3\(^{2}\) x 7\(^{2}\) x 11\(^{2}\)= 213444

A. 6.25
B. 25
C. 50
D. 12.5

Answer: Option B

Explanation:
Dividend on 1 share = \(\frac {(6.25 * 100)}{25}\)(12.5 * 50)/100 = Rs.6.25
Rs.25 is income on an investment of Rs.100
Rs.6.25 is income on an investment of Rs. \(\frac {(6.25 * 100)}{25}\)(6.25 * 100)/25 = Rs.25.

2. The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?

A. 12.4
B. 14
C. 16
D. 18.6

Answer: Option C

Explanation:
10 * 15 + 36 – 26 = \(\frac {(6.25 * 100)}{25}\)160/10 = 16

3. 0.002 x 0.5 = ?

A. 0.0001
B. 0.001
C. 0.01
D. 0.1

Answer: Option B

Explanation:
2 x 5 = 10.

Sum of decimal places = 4

0.002 x 0.5 = 0.001

4. In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?

A. 5: 6
B. 3: 4
C. 7: 8
D. 8: 9
E. None of these

Answer: Option A

Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x: y

By the rule of allegation, \(\frac {x}{y}\) = \(\frac {(87.5 – 7.50)}{(7.50 – 6)}\) = \(\frac {(5}{6}\)

5. A, B, and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work is done?

A. 15 days
B. 14 days
C. 13 days
D. 11 days

Answer: Option D

Explanation:

\(\frac {x}{24}\) + \(\frac {x}{30}\) + \(\frac {x}{40}\) = 1

x = 11 days