1. In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
a) 6
b) 12
c) 18
d) 24
Explanation: Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
2. A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
a) 12
b) 15
c) 18
d) 20
Explanation: Let son's age be x years. Then, father's age = (3x) years.
Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.
So, 3x - 5 = 4 (x - 5) ⇔ 3x - 5 = 4x - 20 ⇔ x = 15.
3. A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?
a) 4/9
b) 5/4
c) 5/8
d) 5/9
Explanation:
4. If you write down all the numbers from 1 to 100, then how many times do you write 3 ?
a) 11
b) 18
c) 20
d) 21
Explanation: Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.
5. If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?
a) 1 day
b) 4 days
c) 40 days
d) 100 days
Explanation:
6. Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What fraction of the bill did Veena pay ?
a) 1/3
b) 3/11
c) 12/13
d) 5/8
Explanation:
7. In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements ?
a) Only 20% of the total members own three cars each
b) 48% of the total members own only one car each.
c) 60% of the total members own at least two cars each.
d) 80% of the total members own at least one car.
Explanation: Let total number of members be 100,
Then, number of members owning only 2 cars = 20.
Number of members owning 3 cars = 40% of 80 = 32.
Number of members owning only 1 car = 100 - (20 + 32) = 48.
Thus, 48% of the total members own one car each.
8. When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
a) 7 years
b) 10 years
c) 14 years
d) 19 years
Explanation:When Rahul was born, his brother's age = 6 years;
His father's age = (6 + 32) years = 38 years,
His mother's age = (38 - 3) years = 35 years;
His sister's age = (35 - 25) years = 10 years.
9. A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there ?
a) 10
b) 12
c) 14
d) 16
Explanation:et number of horses = number of men = x.
Then, number of legs = 4x + 2 x (x/2) = 5x.
So, 5X = 70 or x = 14.
10. Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?
a) 32 years, 23 years
b) 32 years, 29 years
c) 35 years, 29 years
d) 35 years, 33 years
Explanation: When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.