1. The circumferences of the fore and hind-wheels of a carriage are 16 m and 22m respectively. A white mark is put on the point of contact of each wheel with the ground at any given moment. How far will the carriage have travelled so that its white marks may be again on the ground at the same time?
A) 168 m
B) 126 m
C) 174 m
D) 176 m
E) None of these
2. The sum of the present age of the mother and his son is 42 years.7 years later, the mother will be 3 times older than the son. The present age of the mother is:
A) 35
B) 28
C) 32
D) 33
E) None of these
3.
4. The number of gems in three boxes is in the ratio of 3: 4: 5. In which ratio the number of gems in first two baskets must be increased so that the new ratio becomes 5: 4: 3?
A) 1:3
B) 2:1
C) 3:4
D) 2:3
E ) None of these
5. Alloy X contains 40% gold and 60% silver. Alloy Y contains 35% gold and 40% silver and 25% copper. Alloys X and Y are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy is?
A) 20% and 30%
B) 36% and 44%
C) 25% and 35%
D) 49% and 36%
E ) None of these
6. Two integers are chosen at random from a list of 10 consecutive integers. What is the probability that their sum is even?
A) 9/5
B) 9/4
C) 5/4
D) 5/9
E) None of these
7. Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq. meters.
A) 57 m
B) 56 m
C) 59 m
D) 63 m
E ) None of these
8. Find out the length of rectangle if the area of square is 441 cm2and whose side is half the diameter of the circle and whose Circumference is equal to breadth of rectangle and the perimeter of rectangle is 714 cm.
A) 215 cm
B) 167 cm
C) 189 cm
D) 225 cm
E) None of these
Directions (9 - 10) Answer these questions after studying the following table carefully.
Number of workers employed in six units of a factory over the years.
Unit Year |
P |
Q |
R |
S |
T |
U |
2008 |
145 |
88 |
115 |
120 |
140 |
136 |
2009 |
128 |
76 |
122 |
112 |
152 |
132 |
2010 |
136 |
96 |
132 |
124 |
158 |
140 |
2011 |
183 |
92 |
125 |
135 |
166 |
126 |
2012 |
160 |
107 |
140 |
118 |
170 |
146 |
2013 |
152 |
110 |
148 |
128 |
175 |
150 |
9. In the year 2010 the number of workers employed by unit ‘R’ is wheat per cent of the total number of workers employed by all the units in the same year (rounded off to two places of decimal)?
A) 16.39
B) 17.21
C) 16.88
D) 17.31
E) None of these
10.
Question | Answer |
1. | D |
2. | A |
3. | C |
4. | B |
5. | B |
6. | D |
7. | B |
8. | D |
9. | E |
10. | D |
Explanation:1.
A Little reflection will show that white marks will reach the ground together for the first time after the wheels have passed a distance which is the LCM of 16 m and 22 m. LCM of 16 m and 22 m = 176 metres.
Explanation:2. Suppose mother’s present age = X years
Therefore, son’s present age
= (42- X) years [Because the sum of mother’s age & son’s age is 42]
Now, according to the given situation, after 7 years mother will be 3 times older than the son’s age
(X+7) = 3{(42- X) +7}
X+7 = 126-3 X +21
X+3 X= 126+21-7
4 X = 126+21-7
4 X = 140
X = 140/4 =35
Hence, mother’s present age X = 35 years
Explanation:3.
Explanation:4.
Let, Box 1: Box 2 : Box 3 = 3x : 4x : 5x
Again Box1: Box 2 : Box3 = 5y : 4y : 3y
Since there is increase in numbers of gems in first two boxes only, it means the no. of gems remains constant in the third box.
Explanation:5. Assume the weight of alloy X is 100 kg
Therefore the weight of alloy Y is 400kg
Gold silver copper
X 40kg 60kg 0kg
Y 140kg 160kg 100kg
Total 180kg 220kg 100kg
Ratio of gold and silver in new alloy =180/500 : 200/500
= 36%:44%
Explanation:6. There are 5 odd and 5 even numbers in 10 consecutive integers.
If the sum is to be even, the possibilities are:
Either both the integers are odd or
Both of them are even.
The probability is (5/10*5/9)+(5/10*5/9)=5/9
Explanation:8.
Explanation:9.
Explanation:10.