A. 57%
B. 60%
C. 65%
D. 90%

Answer: Option A

Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required percentage = [\(\frac {11628}{20400}\) x 100] % = 57%
R = 5%
I = \(\frac {(450*6*5)}{100}\)= 135
450 + 135 = 585

2. Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

A. Rs. 200
B. Rs. 250

C. Rs. 300

D. None of these

Answer: Option B

Explanation:
Let the sum paid to Y per week be Rs. z.

Then, z + 120% of z = 550.
z + \(\frac {120)}{100}\)Z = 500
\(\frac {11)}{5}\)Z = 550
z = \(\frac {550 x 5)}{11}\) = 250

3. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax-free items?

A. Rs. 15
B. Rs. 15.70
C. Rs. 19.70
D. Rs. 20

Answer: Option C

Explanation:
Let the amount taxable purchases be Rs. x.

Then, 6% of x = \(\frac {30)}{100}\)
x = {\(\frac {30)}{100}\) X \(\frac {100)}{6}\)} = 5
Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70

4. Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

A. Rs. 6876.10
B. Rs. 6876.10
C. Rs. 6654
D. Rs. 7000
E. None of these

Answer: Option A

Explanation:
Rebate = 6% of Rs. 6650 = Rs. [\(\frac {6}{100}\) x 6650] = Rs. 399.

Sales tax = 10% of Rs. (6650 – 399) = Rs. \(\frac {10}{100}\) x 6251] = Rs. 625.10
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10

5. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

A. 4.37%
B. 5%
C. 6%
D. 8.75%

Answer: Option B

Explanation:

Increase in 10 years = (262500 – 175000) = 87500.

Increase% = [\(\frac {87500}{175000}\) x 100]% = 50%.
Required average = \(\frac {50}{10}\)% = 5%

A. 24
B. 27
C. 40
D. Cannot be determined

Answer: Option A

Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.

Then, \(\frac {5x + 3}{4x + 3}\) = \(\frac {11}{9}\)
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x – 44x = 33 – 27
x = 6
Anand’s present age = 4x = 24 years.

2. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

A. 7
B. 8
C. 9
D. 10
E. 11

Answer: Option C

Explanation:
Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years.

(2x + 2) + 2x + x = 27

5x = 25

x = 5.

Hence, B’s age = 2x = 10 years.

3. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A. 14 years

B. 18 years

C. 20 years

D. 22 years

Answer: Option D

Explanation:

Let the son’s present age be x years. Then, man’s present age = (x + 24) years.

(x + 24) + 2 = 2(x + 2)

x + 26 = 2x + 4

x = 22.

4. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?

A. 16 years
B. 18 years
C. 20 years
D. Cannot be determined

Answer: Option A

Explanation:

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then, \(\frac {(6x + 6) + 4}{(5x + 6) + 4 }\) = \(\frac {11}{10 }\)
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.

Sagar’s present age = (5x + 6) = 16 years.

5. The sum of the present ages of a father and his son is 60 years. Six years ago, the father’s age was five times the age of the son. After 6 years, son’s age will be:

A. 12 years

B. 14 years
C. 18 years

D. 20 years

Answer: Option D

Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 – x) – 6 = 5(x – 6)

54 – x = 5x – 30

6x = 84

x = 14.

Son’s age after 6 years = (x+ 6) = 20 years..

A. 12 years
B. 15 years
C. 19 and half
D. 21 years

Answer: Option B

Explanation:
Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,

4x + 6 = 26 4x = 20

x = 5.

Deepak’s age = 3x = 15 years.

2. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A. 16 years
B. 18 years
C. 28 years
D. 24.5 years

Answer: Option D

Explanation:
Let Rahul’s age be x years.

Then, Sachin’s age = (x – 7) years.
\(\frac {x – 7}{x}\)

\(\frac {7}{9}\)
9x – 63 = 7x

2x = 63

x = 31.5
Hence, Sachin’s age =(x – 7) = 24.5 years.

3. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A. 720

B. 900
C. 1200
D. 1800

Answer: Option C

Explanation:
2(15 + 12) x h = 2(15 x 12)
h = \(\frac {180}{27}\)m = \(\frac {20}{3}\)m
Volume = 15 x 12 x \(\frac {20}{3}\)\({m}^{3}\)

4. A boat having a length of 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg

Answer: Option B

Explanation:

Volume of water displaced = (3 x 2 x 0.01) \({m}^{3}\)
0.06 \({m}^{3}\)
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

5. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in \({m}^{3}\)) is:

A. 4830
B. 5120
C. 6420
D. 8960

Answer: Option B

Explanation:

Clearly, l = (48 – 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.
Volume of the box = (32 x 20 x 8) \({m}^{3}\) = 5120 \({m}^{3}\)