Arithmetic (UPSC) Part- IV

Total Questions: 50

1. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A? [2019-II]

(a) 60%
(b) 45.5%
(c) 40%
(d) 37.5%

Correct Answer: (b) 45.5%

Solution:

Let weight of block A = x kg
and weight of block B = y kg
Total weight of two blocks = (x + y) kg
ATQ,

Now, when block B is removed, then percent reduction in the weight =

2. In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football? [2019-II]

(a) 4
(b) 8
(c) 10
(d) 12

Correct Answer: (b) 8

Solution:L.C.M. of 4 and 6 = 12
Hence the number assigned to the students who play cricket as well as football is divisible by 12.
Numbers divisible by 12 are 12, 24, 36...
Total number of such numbers up to 100 = 8
And those are: 12, 24, 36, 48, 60, 72, 84, 96
Hence required number = 8

3. Raju has ₹ 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ₹ 2000 from a friend. Then [2019-II]

(a) Raju still does not have enough amount to buy the handset.
(b) Raju has exactly the same amount as required to buy the handset.
(c) Raju has enough amount to buy the handset and he will have ₹ 500 with him after buying the handset.
(d) Raju has enough amount to buy the handset and he will have ₹ 1000 with him after buying the handset.

Correct Answer: (a) Raju still does not have enough amount to buy the handset.

Solution:

4. In 2002, Meenu’s age was one-third of the age of Meera, whereas in 2010, Meenu’s age was half the age of Meera. What is Meenu’s year of birth? [2019-II]

(a) 1992
(b) 1994
(c) 1996
(d) 1998

Correct Answer: (b) 1994

Solution:

Let Meera age in 2002 = x years
and Meenu age in 2002 = y years
∴ x = 3y and x + 8 = 2(y + 8)

Meenu's age = 8 years
Hence, Meenu's year of birth = 2002 – 8 = 1994

5. Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹1300 and Rajesh spent ₹1500. If each racket costs three times a ball does, then what is the price of a racket? [2019-II]

(a) ₹70
(b) ₹90
(c) ₹210
(d) ₹240

Correct Answer: (c) ₹210

Solution:

Cost of 10 balls + 10 rackets = 1300 + 1500 = 2800
∴ Cost of 1 ball + 1 racket = 280 … (i)

ATQ, Cost of 1 racket = 3 × Cost of 1 ball

From (i):
Cost of 4 balls = 280
Cost of 1 ball = 70
∴ Cost of 1 racket = ₹ 210

6. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? [2019-II]

At least 30 Indian participants are vegetarian.
At least 10 Indian participants are non-vegetarian.
Select the correct answer using the codes given below:

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (c) Both 1 and 2

Solution:

Number of non-Indian participants = 100 – 70 = 30

Number of vegetarian = 60
Number of Indian that are vegetarian ≥ (60 – 30) ≥ 30
Number of non-vegetarian = 100 – 60 = 40
Maximum number of non-Indian that are non-vegetarian = 40 – 30 = 10

7. All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data? [2019-II]

40% members went for shopping as well as sightseeing.
20% members went for only shopping.
Select the correct answer using the code given below:

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (a) 1 only

Solution:

8. The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. The number of such pairs is [2019-II]

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

Correct Answer: (b) 4

Solution:

Let the two-digit natural number be
On reversing its digits, number formed =
ATQ,

Hence, such numbers are (12, 24, 36, 48)

9. In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored? [2019-II]

(a) 360
(b) 380
(c) 400
(d) 420

Correct Answer: (b) 380

Solution:

10. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct? [2019-II]

(a) x is greater than y
(b) (y – x) is greater than 15
(c) (y – x) is less than or equal to 15
(d) (x + y) is greater than or equal to 65

Correct Answer: (c) (y – x) is less than or equal to 15

Solution:

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Arithmetic (UPSC) Part- IV

1. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A? [2019-II]

3. Raju has ₹ 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ₹ 2000 from a friend. Then [2019-II]

4. In 2002, Meenu’s age was one-third of the age of Meera, whereas in 2010, Meenu’s age was half the age of Meera. What is Meenu’s year of birth? [2019-II]

5. Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹1300 and Rajesh spent ₹1500. If each racket costs three times a ball does, then what is the price of a racket? [2019-II]

6. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? [2019-II]

7. All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data? [2019-II]

8. The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. The number of such pairs is [2019-II]

9. In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored? [2019-II]

10. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct? [2019-II]

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