Arithmetic (UPSC) Part- I

Total Questions: 50

31. For the system of equations x² + y² = 34, x⁴ – y⁴ = 544, the values of x and y are [2001]

(a) +4, +, 3
(b) +5, +,3
(c) +3, +, 5
(d) +3, +, 4

Correct Answer: (b) +5, +,3

Solution:The given equations are

x² + y² = 34

= 544 ⇒ (x²)² - (y²)² = 544 ⇒ (x² + y²) (x² - y²) = 544

Putting value of (i) in (ii),

34(x² - y²) = 544 ⇒ x² - y² = 16

Now, checking it with the given options, only $3$ satisfies it.

32. Water is filled in a container in such a manner that its volume doubles after every five minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full? [2001]

(a) 7 minutes and 30 seconds
(b) 10 minutes
(c) 20 minutes
(d) 25 minutes

Correct Answer: (c) 20 minutes

Solution:Container is filled in 30 min.
∴ Container is half-filled in

min
Hence, time taken for the container to be one-fourth filled =

min

33. A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is [2001]

(a) 24,000
(b) 30,000
(c) 54,000
(d) 60,000

Correct Answer: (a) 24,000

Solution:

Literate population = $50$ / $100$ (300000) = 150000

Male literate population = $70/100$ (180000) = 126000

Literate female population = 150000 - 126000 = 24000

34. In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both? [2001]

(a) 65%
(b) 80%
(c) 85%
(d) 97.5%

Correct Answer: (c) 85%

Solution:

Percentage of car owners = 80%
Percentage of mobile phone owners = 60%
Percentage of people having both car and mobile phone = 55%

Percentage of people having only car = 80 – 55 = 25%
Percentage of people having only mobile phone = 60 – 55 = 5%

Percentage of people having a car or a mobile phone or both =
55% + 25% + 5% = 85%

35. In 1930, a person's age was 8 times that of his Son. In 1938, the father's age became ten times that of his son's age in 1930. The ages of the son and father in 1940 were respectively [2001]

(a) 16 years, 58 years
(b) 15 years, 50 years
(c) 14 years, 42 years
(d) 13 years, 34 years

Correct Answer: (c) 14 years, 42 years

Solution:

Let son’s age in 1930 be years
Then father’s age in 1930 will be years
In 1938, father’s age = years

As per the question,

Hence son’s age in 1930 = 4 years
Father’s age in 1930 = years

Therefore, the age of son and father in 1940 will be 14 years and 42 years respectively.

36. Amit started a business by investing ₹30,000. Rahul joined the business after some time and invested ₹20,000. At the end of the year, profit was divided in the ratio of 2:1. After how many months did Rahul join the business? [2002]

(a) 2
(b) 3
(c) 4
(d) 5

Correct Answer: (a) 2

Solution:

Let after months Rahul joined the business.
Hence Amit does business for 1 year and Rahul for months.

They will share the profit in ratio:

30000 × 12:20000 × (12–t) = 2:1

⇒ 360000/240000−20000t = 2/1

⇒ 40000t = 480000 − 360000 ⇒ 40000t = 120000 ⇒ t = 3 months

37. When the time in the wall-clock is 3.25 p.m., the acute angle between the hours-hand and the minutes-hand is [2002]

(a) 60°
(b) 52.5°
(c) 47.5°
(d) 42°

Correct Answer: (c) 47.5°

Solution:In a clock, the angle between two successive numbers is

360∘/12 = 30∘

When the time is 3.25 p.m., the minute hand will be on 5 and will have moved 60° from 3, and the hour hand would be between 3 and 4. As it moves 30° in 60 minutes, so in 25 minutes, it would move

30∘ × 25/60 = 12.50∘

So the difference between two hands will be

38. The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father's present age is [2002]

(a) 40 years
(b) 45 years
(c) 50 years
(d) 55 years

Correct Answer: (b) 45 years

Solution:

39. In a company, 60% of the employees are men. Of these 40% are drawing more than ₹50,000 per year. If 36% of the total employees of the company draw more than ₹50,000 per year, what is the percentage of women who are drawing less than ₹50,000 per year? [2002]

(a) 70
(b) 60
(c) 40
(d) 30

Correct Answer: (a) 70

Solution:Let total number of employees be 100

Number of men=60×100/100 = 60

Number of women=40×100/100 = 40

Number of men drawing more than ₹50,000

= 40 × 60/100 = 24 men

Since number of total employees drawing more than ₹50,000

36 × 100/100 = 36

Number of women who draw more than ₹50,000 = 36 – 24 = 12
Number of women who draw less than ₹50,000 = 40 – 12 = 28

Percentage of women who draw less than ₹50,000 per year

28 ×100/40 =70%

40. A trader fixed the price of an article in such a way that by giving a rebate of 10% on the price fixed, he made a profit of 15%. If the cost of the article is ₹72, the price fixed on it, is [2002]

(a) ₹82.80
(b) ₹90.00
(c) ₹92.00
(d) ₹97.80

Correct Answer: (c) ₹92.00

Solution:Selling price = Cost price (1 + % Gain)
= Marked price (1 – % Discount)

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Arithmetic (UPSC) Part- I

31. For the system of equations x² + y² = 34, x⁴ – y⁴ = 544, the values of x and y are [2001]

32. Water is filled in a container in such a manner that its volume doubles after every five minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full? [2001]

33. A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is [2001]

34. In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both? [2001]

35. In 1930, a person's age was 8 times that of his Son. In 1938, the father's age became ten times that of his son's age in 1930. The ages of the son and father in 1940 were respectively [2001]

36. Amit started a business by investing ₹30,000. Rahul joined the business after some time and invested ₹20,000. At the end of the year, profit was divided in the ratio of 2:1. After how many months did Rahul join the business? [2002]

37. When the time in the wall-clock is 3.25 p.m., the acute angle between the hours-hand and the minutes-hand is [2002]

38. The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father's present age is [2002]

39. In a company, 60% of the employees are men. Of these 40% are drawing more than ₹50,000 per year. If 36% of the total employees of the company draw more than ₹50,000 per year, what is the percentage of women who are drawing less than ₹50,000 per year? [2002]

40. A trader fixed the price of an article in such a way that by giving a rebate of 10% on the price fixed, he made a profit of 15%. If the cost of the article is ₹72, the price fixed on it, is [2002]

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