Arithmetic (UPSC) Part- I

Total Questions: 50

21. Amar, Akbar and Anthony are friends, being looked after by a matron Farah. Amar weighs 50% more than Akbar and Anthony weighs 25% less than Amar. Farah weighs a third of the combined weight of the three boys. All four together weigh 232 kg. The correct arrangement of the persons in the ascending order of their weights, is: [1999]

(a) Anthony, Akbar, Farah, Amar
(b) Anthony, Akbar, Amar, Farah
(c) Akbar, Anthony, Amar, Farah
(d) Akbar, Anthony, Farah, Amar

Correct Answer: (d) Akbar, Anthony, Farah, Amar

Solution:

Let weight of Akbar = kg.

Then weight of Amar =

and weight of Anthony =

Hence weight of Farah =

According to question

22. In the sequence of numbers 5, 8, 13, X, 34, 55, 89, ..., the value of X is [1999]

(a) 19
(b) 21
(c) 23
(d) 29

Correct Answer: (b) 21

Solution:Given pattern:
A number is obtained by summation of previous two numbers.
13 = 8 + 5, X = 8 + 13 = 21, 21 + 34 = 55 and so on.

23. In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a phone and a car. [1999]

Consider the following statements in this regard:

10% families own both a car and a phone
35% families own either a car or a phone
40,000 families live in the town

Which of the above statements are correct?

(a) 1 & 2
(b) 1 & 3
(c) 2 & 3
(d) 1, 2 & 3

Correct Answer: (c) 2 & 3

Solution:

Suppose x% families own both a car and a phone, then
Percentage of the families owning only a phone = 25 – x
Percentage of the families owning only a car = 15 – x

∴ Now, (25 – x) + (15 – x) + x + 65 = 100
⇒ x = 5

Percentage of families who have either a car or a phone
= (25 – 5) + (15 – 5) + 5 = 35
So statement (2) is correct.

Let the total number of families in the town be y.

So statement (3) is also correct.

24. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics? [2000]

(a) 750
(b) 500
(c) 250
(d) 125

Correct Answer: (b) 500

Solution:

Let x% candidates take both the subjects.
Percentage of candidates who opted for Physics = 65.8%
Percentage of candidates who opted for Mathematics = 59.2%

Now, total number of candidates = 2000
∴ Number of candidates who opted for both the subjects =

25 × 2000/100 = 50

25. A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club? [2000]

(a) 20
(b) 24
(c) 27
(d) 30

Correct Answer: (c) 27

Solution:No. of women =

∴ No. of married women = No. of women – No. of unmarried women
=

36 - 9 = 27

26. An accurate clock shows 8 o'clock in the morning. Throughout how many degrees will the hour hand rotate, when the clock shows 2 o'clock in the afternoon? [2000]

(a) 150°
(b) 144°
(c) 168°
(d) 180°

Correct Answer: (d) 180°

Solution:Angle made by hour hand for 12 hours =

Angle made by hour hand for 1 hour =

∴ Angle made by hour hand for 6 hours =

27. The monthly income of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save ₹600 per month. What is their total monthly income? [2000]

(a) ₹8,400
(b) ₹5,600
(a) ₹8,400
(d) ₹2,800

Correct Answer: (b) ₹5,600

Solution:

Let monthly income of Komal and Asha be 4x and 3x
Also, let monthly expenses of Komal and Asha be 3y and 2y.

Now,

4x − 3y = 600 (i)

3x − 2y = 600 (ii)

Solving (i) and (ii),
∴ Total monthly income =

28. If x = –2, then x³ – x² – x – 1 is equal to [2000]

(a) 1
(b) –3
(c) –11
(d) –15

Correct Answer: (c) –11

Solution:(−2)³−(−2)²−(−2)−1 = − 11

29. The given diagram shows the number of students who failed in an examination comprising papers in English, Hindi and Mathematics. The total number of students who took the test is 500. What is the percentage of students who failed in at least two subjects? [2000]

(a) 6.8
(b) 7.8
(c) 34
(d) 39

Correct Answer: (b) 7.8

Solution:

No. of students who failed in Hindi and English = 10

No. of students who failed in English and Maths = 12

No. of students who failed in Maths and Hindi = 12

No. of students who failed in Maths, English and Hindi = 5

∴ Total No. of students who failed in at least two subjects
= No. of students failed in any two subjects + No. of students failed in 3 subjects
=

∴ % of students failed in at least 2 subjects = 39/500 ×100 = 7.8

30. In a class there are 18 boys who are over 160 cm tall. If these boys constitute three fourths of the boys and the total number of boys is two-thirds of the number of students in the class, then what is the number of girls in the class? [2000]

(a) 6
(b) 12
(c) 18
(d) 24

Correct Answer: (b) 12

Solution:

Let the total No. of boys be $n$ .
Now, number of boys above 160 cm height = 18

Also, let total no. of students be $N$ .

∴ Number of girls =

« Previous 1 234 5 Next »

Arithmetic (UPSC) Part- I

22. In the sequence of numbers 5, 8, 13, X, 34, 55, 89, ..., the value of X is [1999]

23. In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a phone and a car. [1999]

24. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics? [2000]

25. A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club? [2000]

26. An accurate clock shows 8 o'clock in the morning. Throughout how many degrees will the hour hand rotate, when the clock shows 2 o'clock in the afternoon? [2000]

27. The monthly income of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save ₹600 per month. What is their total monthly income? [2000]

28. If x = –2, then x³ – x² – x – 1 is equal to [2000]

29. The given diagram shows the number of students who failed in an examination comprising papers in English, Hindi and Mathematics. The total number of students who took the test is 500. What is the percentage of students who failed in at least two subjects? [2000]

30. In a class there are 18 boys who are over 160 cm tall. If these boys constitute three fourths of the boys and the total number of boys is two-thirds of the number of students in the class, then what is the number of girls in the class? [2000]

Related Posts