Arithmetic (UPSC) Part- III

Total Questions: 50

11. The monthly average salary paid to all the employees of a company was ₹5000. The monthly average salary paid to male and female employees was ₹5200 and ₹4200 respectively. Then the percentage of males employed in the company is: [2016-II]

(a) 75%
(b) 80%
(c) 85%
(d) 90%

Correct Answer: (b) 80%

Solution:Let the number of employees in the company be 100 and the number of male employees in the company be x.
So, the number of female employees = 100 – x.
According to the question,
(5200x + 4200(100 – x)) / 100 = 5000

⇒ 52x + 42 (100 – x) = 5000
⇒ 52x + 4200 – 42x = 5000
⇒ 10x + 800 ⇒ x = 80
So, there are 80% male employees in the company.

12. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X? [2016-II]

(a) 12%
(b) 10%
(c) 9%
(d) 8%

Correct Answer: (b) 10%

Solution:Let the third number Z = 100
So, X = 80, Y = 72
∴ Percentage by which Y is less than X
= (80 – 72) / 80 × 100 = 10%

13. What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150 [2017-II]

(a) 262
(b) 342
(c) 360
(d) 450

Correct Answer: (d) 450

Solution:Number of digits used For 1 – 9 = 9 × 1 = 9
Number of digits used For 10 – 99 = 90 × 2 = 180
Number of digits used for 100 – 150 = 51 × 3 = 153
Hence, 153 + 180 + 9 = 342 digits.

14. If there is a policy that 1/3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period? [2017-II]

(a) 16/243rd part of the population
(b) 32/243rd part of the population
(c) 32/729th part of the population
(d) 64/729th part of the population

Correct Answer: (d) 64/729th part of the population

Solution:Population of the Community after every year = 2/3 of
the previous year. Hence, the population of the community
after 6 year = (2/3)⁶ of the original population of the

Community. (2/3)⁶ = 64/729 th part.

15. There are three pillars, X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar? [2017-II]

(a) 161 cm
(b) 163 cm
(c) 182 cm
(d) 210 cm

Correct Answer: (b) 163 cm

Solution:Distance travelled by A in one chance
= (6 – 1) cm = 5 cm
Distance travelled by B in one chance
= (7 – 3) cm = 4 cm
Distance travelled by C in one chance
= (6.5 – 2) cm = 4.5 cm.
Hence, Length of pillar X = 5 × 39 + 6 = 201 cm
Length of pillar Y = 4 × 39 + 7 = 163 cm
Length of pillar Z = 4.5 × 39 + 6.5 = 182 cm
Length of shortest pillar → Y = 163 cm.

16. Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal's position if he agreed? [2017-II]

(a) Neither loss nor gain
(b) Loss 1%
(c) Gain 1%
(d) Gain 0.5%

Correct Answer: (c) Gain 1%

Solution:Let the original price of phone = ₹100
SP of Gopal = 100 × 110 / 100 = ₹110

SP of Ram = 110 – 10% of 110 = ₹99
Total Profit of gopal = ₹100 – ₹99 = 1
But profit was made as CP hence, 1% profit

17. Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the 5th person will be [2017-II]

(a) 45 kg
(b) 47.5 kg
(c) 50 kg
(d) 52.5 kg

Correct Answer: (c) 50 kg

Solution:The weight of the 5th person = sum of first 5 person + Sum of last five person – Sum of weight of 9 persons.
= 5 × 45 + 5 × 55 – 9 × 50 kg = 50 kg

18. A watch loses 2 minutes in every 24 hours, while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is followed? [2017-II]

(a) The two watches show the identical time again on completion of 30 days.
(b) The two watches show the identical time again on completion of 90 days.
(c) The two watches show the identical time again on completion of 120 days.
(d) None of the above statements is correct.

Correct Answer: (d) None of the above statements is correct.

Solution:None of the above statement is correct.

19. In a city, 12% of households earn less than ₹30,000 per year, 6% households earn more than ₹2,00,000 per year, 22% households earn more than ₹1,00,000 per year and 990 households earn between ₹30,000 and ₹1,00,000 per year. How many households earn between ₹1,00,000 and ₹2,00,000 per year? [2017-II]

(a) 250
(b) 240
(c) 230
(d) 225

Correct Answer: (b) 240

Solution:12% earn less than ₹ 30,000.
6% earn more than ₹ 2,00,000.
22% earn more than ₹ 1,00,000.
So, between ₹ 30,000 – ₹ 1, 00, 000 there are
(100 – 22 – 12)% = 66% household.
66% household is equal to 990
Hence, Number of household = 1500.
Number of household between 1,00,000 and 2,00,000
= 1500 × 16 / 100 = 240.

20. A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock? [2017-II]

(a) 20 seconds
(b) 24 seconds
(c) 28 seconds
(d) 30 seconds

Correct Answer: (b) 24 seconds

Solution:At 5 O’clock the clock will strike 5 times. It’s given
that it takes 12 seconds to do so.
Now, at 10 O' clock the clock will strike 10 times. Hence,
the time taken by it to strike
= 12 / 5 × 10 = 24 seconds.

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