ARITHMETICAL REASONING (General Mental Ability) UPSC EPFO

Total Questions: 24

1. Hari is twice as old as Johnny, who is three years older than Rahul. If Hari’s age is five times Rahul’s age, how old is Johnny?

Correct Answer: (c) 5 years
Solution:

Suppose the age of Johnny is F years and that of Rahul
is y years.
According to question
Age of Hari
⇒ 2F – 5y
or, 2F – 5y = 0 ...                                                          (i)
Again F = 3 + y
or, F – y = 3 ...                                                             (ii)
On solving equations (i) and (ii), we get
y = 2
∴ Age of Johny = 3 + y = 3 + 2 = 5 years

2. A bus leaves Delhi with half the number of women as men. At Meerut, ten men get down and five women get in. Now there are equal number of men andwomen. How many passengers boarded the bus initially at Delhi?

Correct Answer: (b) 45
Solution:

Suppose the number of women boarded the bus at
Delhi is F.
Therefore, the number of men= 2F
According to question,
2F – 10 = F + 5
⇒ 2 F – F = 10 + 5
Q F = 15
Total number of passengers
boarded the bus initially
= 3 F = 3 × 15 = 45

3. A bus left with some definite number of passengers. At the first stop, half of the passengers left the bus and 35 boarded the bus. At the second stop 1/5 of the passengers left and 40 boarded the bus. Then, the bus moved with 80 passengers towards its destination without stopping anywhere. How many passengers were there originally?

Correct Answer: (b) 30
Solution:

4. There are three baskets of fruits. First basket has twice the number of fruits in the 2nd basket. Third basket has 3/4th of the fruits in the first. The average of the fruits in all the baskets is 30. What is the number of the fruits in the first basket?

Correct Answer: (d) 40
Solution:

5. The average age of 19 boys in a class is 21 years. If the teacher’s age is included, the average increases to 22 years. What is the teacher’s age?

Correct Answer: (b) 41 years
Solution:

Total age of 19 boys = 19 × 21 = 399 year
Total age including teacher’s = 20 × 22 = 440
∴ Teacher’s age = 440 – 399 = 41 years

6. A father tells his son, “I was three times of your present age when you were born.” If the father’s present age is 48 years, how old was the boy 4 years ago?

Correct Answer: (b) 8 years
Solution:

Present age of the son = 12 years The father was 36
years old when the boy was born.
= 12 × 3 = 36 years
0 + 12 = 12 years
and 36 + 12 = 48 years

7. In a family Mr. Prakash has his wife and his two married brothers of whom one has two children and another has no issue. How many members are there in the family?

Correct Answer: (b) 8 members
Solution:

Mr. Prakash and his wife = 2
Prakash’s two married brothers = 4
Two children = 2
Total members = 2 + 4 + 2 = 8

8. A two member committee comprising one male and one female member is to be constituted out of five males and three females. Amongst the females, Mrs. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?

Correct Answer: (d) 14
Solution:

Total number of ways in which the committee can be
formed = 5 × 3 = 15
But Ms. A refuses to be a member of the committee in
which Mr. B is taken as a member.
Therefore, the required answer = 15 –1 = 14

9. Out of 100 families in the neighbourhood, 50 members have radios, 75 members have TVs and 25 members have VCRs. Only 10 families have all three and each VCR owner also has a TV. If some families have radio only, how many have only TV?

Correct Answer: (c) 40
Solution:

25 have VCRs and each VCR owner also has a TV.
Therefore, the TV owners who have not VCRs
= 75 – 25 = 50 = 75 – 25 = 50
Now, 10 have all the three.
Therefore, 50 – 10 = 40 have only TV.

10. In a certain office, 1/3 of the workers are women, 1/2 of the someone married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, then what part of workers are without children?

Correct Answer: (c) 11/18
Solution: