Arithmetic (UPSC) Part- I

Total Questions: 50

1. In track meets both 100 yards and 100 metres are used as 1 distances; By how many metres is 100 metres longer than 100 yards? [1995]

(a) 0.856 m
(b) 8.56 m
(c) 0.0856 m
(d) 1.0 m

Correct Answer: (b) 8.56 m

Solution:1 yard = 36 inches

1 inch = 2.54 cm

∴ 1 yard = 2.54 × 36 cm

∴ 100 yard = 2.54 × 36 /100 × 100 = 91.44 m.

Difference (100m – 100 yards) = (100 – 91.44)m = 8.56 m.

2. The value of (a – m) (b – m)….. (y – m) (z – m) is [1995]

(a) m²⁶ + am²⁵ + abm²⁴ + … + a.b.c … z
(b) m²⁶ – am²⁵ + abm²⁴ + … + a.b.c … z
(c) 0
(d) indeterminate

Correct Answer: (c) 0

Solution:(a – m) (b – m) (c – m) ..... (m – m) ..... (z – m) = 0 (∴ (m – m) = 0)

3. Out of a total of 120 musicians in a club, 5% can play all the 1 three instruments, guitar, violin and flute. If so happens that the number of musicians who can play any two or only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone? [1995]

(a) 45
(b) 44
(c) 38
(d) 30

Correct Answer: (b) 44

Solution:Total number of musicians = 120

Number of musicians who can play all the three instruments = 5% of 120 = 5/100 × 120 = 6

Number of musicians who can play any two or only two of three instruments = 30 Number of the musicians who can play the guitar alone = 40

Now the number of musicians who can play violin alone or flute¹ alone = Total number of musician – the number of musicians in all three categories

= 120 – (30 + 40 + 6) = 120 – 76 = 44

4. A person earns ₹ 2000 per month over and above his salary as additional charge allowance. However, 30% of this additional income will be deducted as additional income tax at source. If the person would deposit ₹ 1000 per month on a long term saving fetching 12% interest his tax liability on the additional allowance would reduce to 10%. What is the effective interest for this person for money invested in the long term savings scheme? [1995]

(a) 12%
(b) 18%
(c) 19%
(d) 20%

Correct Answer: (b) 18%

5. The average of x₁, x₂ and x₃ is 14. Twice the sum of x₂ and x₃ is 30. What is the value of x₁? [1996]

(a) 20
(b) 27
(c) 16
(d) 2

Correct Answer: (b) 27

Solution:x₁ + x₂ + x₃/3 = 14

x₂ + x₃ = 42 – x₁ .......(i)

2(x₂ + x₃) = 30

x₂ + x₃ = 15 .......(ii)

Putting (i) in (ii), x₁ = 27

6. If the price of a television set is increased by 25%, then by what percentage should the new price be reduced to bring the price back to the original level? [1996]

(a) 15%
(b) 25%
(c) 20%
(d) 30%

Correct Answer: (c) 20%

Solution:Let the original price be x.

Increased price = x (1 + 25/100) = 5x/4

Reduction in price to bring it back to its original value = 5x/4 - x = x/4

% Reduction = (x/4)/(5x/4)×100 = 20%

7. www.takshilaonline.com If A = x² – y², B = 20 and x + y = 10, then [1996]

(a) A is greater than B
(b) B is greater than A
(c) A is equal to B
(d) Data provided is inadequate

Correct Answer: (d) Data provided is inadequate

Solution:A = x² - y² = (x + y)(x - y) = 10 (x - y) B = 20

Now, it is not possible to compare A and B, as the value of x and y is not known.

8. The average monthly income of person in a certain family of 5 Persons is ₹1000. What will be monthly average income of person in the same family if the income of one person increased by ₹12000 per year? [1997]

(a) ₹1200
(b) ₹1600
(c) ₹2000
(d) ₹3400

Correct Answer: (a) ₹1200

Solution:Total income of the family per month = 5 × 1000 = ₹5000 per month

Increased amount = 12000/12 = ₹1000 per month

Now total amount of the family per month = ₹6000

So the average income of the family per month (after increasing) = 6000/5 = ₹1200

9. In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group? [1997]

(a) 21
(b) 22
(c) 23
(d) 24

Correct Answer: (d) 24

Solution:Total number of Hindi, Tamil and Gujrati speaking people = 15 + 6 + 6 = 27

Two persons of this group can speak 2 languages while one can speak 3 languages.

The third person who knows 3 languages can also speak 2 languages.

He should not be called on two places

Hence, number persons = 27 – 3= 24

10. A survey was conducted on a samples of 1000 persons with reference to their knowledge of English, French and German. The results of the survey are presented in the given Venn diagram. The ratio of the number of the persons who do not know any of the three languages to those who know all the three language, is [1997]

(a) 1/27
(b) 1/25
(c) 1/550
(d) 175/1000

Correct Answer: (b) 1/25

Solution:Total number of persons who know only English or french or German = 170 + 180 + 200 = 550

Number of persons who know any two languages = 105 + 85 + 78 = 268

Number of persons who know all the three languages = 175

∴ Number of persons who know any of the language = 550 + 268 + 175 = 993

Number of persons who do not know any of the language = 1000 – 993 = 7

∴ Required ratio = 7/175 = 1/25

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