1.    The digit in the unit's place of a three digit number is thrice the digit in the ten's place and the digit in the hundred's place is half of the digit in the ten's place. If the sum of the three digits of the number is 9, what is the three digit number?
(1) 243                               (2) 713
(3) 126                               (4) None of these
(5) Cannot be determined

2.    If the persons A and B have incomes in the ratio 7 : 5 and expenditures in the ratio 3 : 2 and each one of them saves Rs P, then, the income of B is:
(1) P                                  (2) 7P
(3) 7/2 P                            (4) 5P
(5) None of these

3.    A train running at 36 km/hr passes another train completely in 12 s, which is half of its length, running in the opposite direction at 54 km/hr. If it also passes a railway platform in 1.5 min, what is the length of the platform (in metres)?
(1) 700                               (2) 860
(3) 900                               (4) 1, 000
(5) None of these

4.    2 rice varieties costing Rs 20 per kg and Rs 30 per kg were mixed as 2 : 3 and sold so as to gain 10%. What was the SP of the mixture (Rs/kg)?
(1) 31.2                              (2) 28.6
(3) 30                                 (4) 26
(5) 32.6

5.    A circle of radius 8 cm has its radius decreased by 2 cm. What is the approximate percentage decrease in area?
(1) 25%                             (2) 50%
(3) 38%                             (4) 43.75%
(5) None of these

6.    In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?
(1) 1520                             (2) 1250
(3) 2008                             (4) 2800
(5) None of these

7.    The ratio of the present ages of Sonu and Monu is 7 : 6 respectively. Eight years ago the respective ratio of their ages was 5 : 4. What will be Monu’s age four years from now?
(1) 28 years                       (2) 32 years
(3) 24 years                       (4) 30 years
(5) None of these

8.     The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?
(1) 7                                   (2) 9
(3) 11                                 (4) 5

9.    A invests Rs. 24000 to start a business. Four months later B joins him by investing Rs. 31000 and after another two months C joins them by investing Rs. 40000. At the end of one year the business earns a profit of Rs. 12028. What is C's share in the profit ?
(1) Rs. 4464                      (2) Rs. 3844
(3) Rs. 3720                      (4) Rs. 3270
(5) None of these

10.  2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
(1) 4                                   (2) 8
(3) 6                                   (4) 2
(4) None of these

1.    (3) Let the ten’s place = x
Then unit place = 3x
And hundreds place = x/2
Now,
x + 3x + x/2 = 9
x = 2
Hence the number is 126

2.    (4) Let the incomes of A and B be 7x and 5x respectively. Then the expenditures of A and B are 7x – P and 5x – p respectively. Now
7x – P/ 5x – P = 3/2

x = P
Hence income of B is 5P

3.    (1)
Crossing time = l1+ l2 / relative speed
l1 = x
l2 = x/2

Relative speed = 36 + 54 = 90 km/hr = 90 x 5/8 = 25 m/s
Time = 12 sec
12 = x + x/2 / 25

x = 200 m
Now train crossing the platform
l1 = 200 m,    l2 = length of platform = y

Time = 1.5 min = 90 sec
Speed = 36 km/hr = 10 m/s
90 = 200 + y / 10

Y = 700 m

4.    (2) CP of the mixture = 20 x 2 + 30 x 3  / 5   = 26
SP = 1.1 x 6 = 28.6

5.    (4) Original area of the circle = Ï€ (8)2 = 64 Ï€
New area of the circle = Ï€ (6)2 = 36 Ï€

% decrease in area = 64 Ï€  - 36 Ï€ / 64 Ï€ x 100 = 43.75%

6.    (5) Total Students in school = 3600
Number of boys = 4/9 x 3600 = 1600
Number of boys who like hockey = 20% of 1600 = 320
Number of girls = 2000
Number of girls who like hockey = 60% of 2000 = 1200
Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080

7.    (1)Let the present ages of Sonu and Monu be 7x and 6x. Now
7x – 8 /6x – 8 = 5/4

x = 4
Present age of Monu = 24 years
Monu’s age four years from now = 24 + 4 = 28 years

8.    (2) Let the numbers be x, x + 2 and x + 4. Then
x + (x + 2) + (x + 4) = x + 20
x = 7
So the middle number is 9.

9.    (3) The ratio of their investments = 24000 x 12: 31000 x 8 : 40000x6 = 36 : 31:30

Since the ratio of investment is also the ratio of profit,
C’s share = 30/97 x 12028 = 3720

10.  (2) 2 M x 6 = 2 W x 9 = 3 C x 8
2 M = 3 W = 4 C

The ratio of efficiencies of man, woman and children = 1/2 : 1/3 : 1/4
= 6 : 4 : 3
Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.
So the total work to be done = 2x6x6 = 72 units

Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units

Remaining work = 72 – 24 = 48 units

Number of men required to complete the remaining work in one day = 48/6 = 8