Practice | Hashtable

31. Study the following table carefully and answer the questions that follow:
Semester fees (In Rs. thousands) for five Different Courses in 6 different years.

Year Course

B. Tech. M.Sc. B. Ed. M. Phil. Diploma

2005 11.5 5.8 7.5 4.7 1.8

2006 14.5 6.4 11.6 5.8 3.2

2007 20.0 10.2 13.9 8.6 4.8

2008 22.2 14.6 15.8 12.7 5.6

2009 35.8 17.7 18.5 25.1 12.5

2010 50.7 20.9 22.6 18.9 14.9

What was the average semester fee charged for M. Sc. course over all the years together?

A. Rs. 12700

B. Rs. 12600

C. Rs. 12060

D. Rs. 12070

Discuss

Solution:

Average semester fee for M. Sc. course over the give years.

= \frac{(5.8 + 6.4 + 10.2 + 14.6 + 17.7 + 20.9) \times 1000}{6}

\begin{aligned} = \frac{75.6 \times 1000}{6} \\ = \frac{75600}{6} \\ = Rs. 12600 \end{aligned}

32. Study the following table carefully and answer the questions that follow:
Semester fees (In Rs. thousands) for five Different Courses in 6 different years.

Year Course

B. Tech. M.Sc. B. Ed. M. Phil. Diploma

2005 11.5 5.8 7.5 4.7 1.8

2006 14.5 6.4 11.6 5.8 3.2

2007 20.0 10.2 13.9 8.6 4.8

2008 22.2 14.6 15.8 12.7 5.6

2009 35.8 17.7 18.5 25.1 12.5

2010 50.7 20.9 22.6 18.9 14.9

What was the total semester fee charged for all the course together in the year 2006?

A. Rs. 42500

B. Rs. 41500

C. Rs. 41600

D. Rs. 42200

Discuss

Solution:

Total semester fee for all the courses in 2006
= Rs. (14.5 + 6.4 + 11.6 + 5.8 + 3.2) × 1000
= Rs. (41.5 × 1000)
= Rs. 41500

33. Study the following table carefully and answer the questions that follow:
Semester fees (In Rs. thousands) for five Different Courses in 6 different years.

Year Course

B. Tech. M.Sc. B. Ed. M. Phil. Diploma

2005 11.5 5.8 7.5 4.7 1.8

2006 14.5 6.4 11.6 5.8 3.2

2007 20.0 10.2 13.9 8.6 4.8

2008 22.2 14.6 15.8 12.7 5.6

2009 35.8 17.7 18.5 25.1 12.5

2010 50.7 20.9 22.6 18.9 14.9

What was the approximate per cent increase in the semester fees of B. Ed. course in the year 2007 as compared to the previous year?

A. 26%

B. 30%

C. 20%

D. 16%

Discuss

Solution:

Percent increase in semester fees of B. Ed. in the year 2007 as compared to 2006.

\begin{aligned} = {\frac{(13.9 - 11.6)}{11.6} \times 100} % \\ = (\frac{2.3}{11.6} \times 100) % \\ = \frac{2300}{116} % \\ = \frac{575}{29} % \\ = 19.8 % \\ \approx 20 % \end{aligned}

34. Study the following table carefully and answer the questions that follow:
Semester fees (In Rs. thousands) for five Different Courses in 6 different years.

Year Course

B. Tech. M.Sc. B. Ed. M. Phil. Diploma

2005 11.5 5.8 7.5 4.7 1.8

2006 14.5 6.4 11.6 5.8 3.2

2007 20.0 10.2 13.9 8.6 4.8

2008 22.2 14.6 15.8 12.7 5.6

2009 35.8 17.7 18.5 25.1 12.5

2010 50.7 20.9 22.6 18.9 14.9

What was the difference between the total semester fee charged for diploma course over the years together and the fee charged for B. Tech Course in the year 2009?

A. Rs. 8500

B. Rs. 8000

C. Rs. 6500

D. Rs. 7000

Discuss

Solution:

Required difference
= Rs. {(1.8 + 3.2 + 4.8 + 5.6 + 12.5 + 14.9) × 1000 - (35.8 × 1000)}
= Rs. {(42.8 × 1000) - (35.8 × 1000)}
= Rs. (7 × 1000)
= Rs. 7000

35. Study the following table carefully and answer the questions that follow:
Semester fees (In Rs. thousands) for five Different Courses in 6 different years.

Year Course

B. Tech. M.Sc. B. Ed. M. Phil. Diploma

2005 11.5 5.8 7.5 4.7 1.8

2006 14.5 6.4 11.6 5.8 3.2

2007 20.0 10.2 13.9 8.6 4.8

2008 22.2 14.6 15.8 12.7 5.6

2009 35.8 17.7 18.5 25.1 12.5

2010 50.7 20.9 22.6 18.9 14.9

The semester fee charged for M. Phil course in the year 2008 was approximately what percentage of the semester fee charged for M. Sc course in the year 2009?

A. 67%

B. 84%

C. 80%

D. 76%

Discuss

Solution:

\begin{aligned} Required Percentage \\ = {\frac{(12.7 \times 1000)}{(17.7 \times 1000)} \times 100} % \\ = (\frac{127}{177} \times 100) % \\ = \frac{12700}{177} % \\ = 71.75 % \\ \approx 72 % (Approx) \end{aligned}

36. Study the following table carefully and answer the question that follow:
Number of candidates (in lakhs) appearing in a Entrance Examination from six different Cities.

City A B C D E F

No. of Candidates 1.25 3.14 1.08 2.27 1.85 2.73

Ratio of Candidates Passing and Failing Within the City

City Ratio of Passing and Failing

A 7 : 3

B 5 : 3

C 4 : 5

D 1 : 3

E 3 : 2

F 7 : 5

The number of candidates appearing for the exam from City C is what per cent of the number of candidates appearing for the exam from City B? (rounded to nearest integer)

A. 27%

B. 34%

C. 42%

D. 21%

Discuss

Solution:

\begin{aligned} No. of candidates from city C \\ = 1.08 \times 100000 \\ = 108000 \\ No. of candidates from city B \\ = 3.14 \times 100000 \\ = 314000 \\ ∴ Required percentage \\ = (\frac{108000}{314000} \times 100) % \\ = (\frac{108}{314} \times 100) % \\ = (\frac{54}{157} \times 100) % \\ = \frac{5400}{157} % \\ = 34.39 % \\ \approx 34 % \end{aligned}

37. Study the following table carefully and answer the question that follow:
Number of candidates (in lakhs) appearing in a Entrance Examination from six different Cities.

City A B C D E F

No. of Candidates 1.25 3.14 1.08 2.27 1.85 2.73

Ratio of Candidates Passing and Failing Within the City

City Ratio of Passing and Failing

A 7 : 3

B 5 : 3

C 4 : 5

D 1 : 3

E 3 : 2

F 7 : 5

What is the number of candidates passing the exam from city E?

A. 13000

B. 1110000

C. 113000

D. 11000

Discuss

Solution:

Number of candidates passing the exam from City E.

\begin{aligned} = 1.85 \times 100000 \times \frac{3}{5} \\ = 185000 \times \frac{3}{5} \\ = 37000 \times 3 \\ = 111000 \end{aligned}

38. Study the following table carefully and answer the question that follow:
Number of candidates (in lakhs) appearing in a Entrance Examination from six different Cities.

City A B C D E F

No. of Candidates 1.25 3.14 1.08 2.27 1.85 2.73

Ratio of Candidates Passing and Failing Within the City

City Ratio of Passing and Failing

A 7 : 3

B 5 : 3

C 4 : 5

D 1 : 3

E 3 : 2

F 7 : 5

The number of candidates passing the examination from City F is what per cent of the total number of candidates appearing from all the cities together? ( rounded off to two digits after the decimal)

A. 12.93%

B. 14.46%

C. 10.84%

D. 11.37%

Discuss

Solution:

Total number of candidates from al the 5 cities
= {(1.25 + 3.14 + 1.08 + 2.27 + 1.85 + 2.73) × 100000}
= 12.32 × 100000
= 1232000
Number of candidates passing the exam from city F

\begin{aligned} = \frac{7}{12} \times 2.73 \times 100000 \\ = \frac{7 \times 273 \times 1000}{12} \\ = 7 \times 91 \times 250 \\ = 159250 \\ ∴ Required percentage \\ = (\frac{159250}{1232000} \times 100) % \\ = \frac{15925}{1232} % \\ = 12.926 % \\ \approx 12.93 % \end{aligned}

39. Study the following table carefully and answer the question that follow:
Number of candidates (in lakhs) appearing in a Entrance Examination from six different Cities.

City A B C D E F

No. of Candidates 1.25 3.14 1.08 2.27 1.85 2.73

Ratio of Candidates Passing and Failing Within the City

City Ratio of Passing and Failing

A 7 : 3

B 5 : 3

C 4 : 5

D 1 : 3

E 3 : 2

F 7 : 5

What is the ratio of the number of candidates failing the exam from City D to that of those failing the exam from City A?

A. 289 : 42

B. 42 : 289

C. 227 : 50

D. 50 : 227

Discuss

Solution:

\begin{aligned} No. of candidates failing from city D \\ = \frac{3}{4} \times 2.27 \times 100000 \\ = \frac{3}{4} \times \frac{227}{100} \times 100000 \\ = 227 \times 750 \\ No. of candidates failing from city A \\ = \frac{3}{10} \times 1.25 \times 100000 \\ = \frac{3}{10} \times \frac{125}{100} \times 100000 \\ = 300 \times 125 \\ ∴ Required ratio \\ = \frac{227 \times 750}{300 \times 125} \\ = \frac{227}{50} \\ = 227 : 50 \end{aligned}

40. Study the following table carefully and answer the question that follow:
Number of candidates (in lakhs) appearing in a Entrance Examination from six different Cities.

City A B C D E F

No. of Candidates 1.25 3.14 1.08 2.27 1.85 2.73

Ratio of Candidates Passing and Failing Within the City

City Ratio of Passing and Failing

A 7 : 3

B 5 : 3

C 4 : 5

D 1 : 3

E 3 : 2

F 7 : 5

Which city has the highest number of students failing the entrance exam?

A. F

B. C

C. B

D. D

Discuss

Solution:

Number of failures from different cities:

\begin{aligned} A \to 1.25 \times 100000 \times \frac{3}{10} \\ = 37500 \\ B \to 3.14 \times 100000 \times \frac{3}{8} \\ = \frac{314000 \times 3}{8} \\ = 117750 \\ C \to 1.08 \times 100000 \times \frac{5}{9} \\ = 108000 \times \frac{5}{9} \\ = 60000 \\ D \to 2.27 \times 100000 \times \frac{3}{4} \\ = 227000 \times \frac{3}{4} \\ = 170250 \\ E \to 1.85 \times 100000 \times \frac{2}{5} \\ = 185000 \times \frac{2}{5} \\ = 74000 \\ F \to 2.73 \times 100000 \times \frac{5}{12} \\ = 273000 \times \frac{5}{12} \\ = 113750 \end{aligned}

So,
The maximum number failures are from city D.

Year	Course
Year	B. Tech.	M.Sc.	B. Ed.	M. Phil.	Diploma
2005	11.5	5.8	7.5	4.7	1.8
2006	14.5	6.4	11.6	5.8	3.2
2007	20.0	10.2	13.9	8.6	4.8
2008	22.2	14.6	15.8	12.7	5.6
2009	35.8	17.7	18.5	25.1	12.5
2010	50.7	20.9	22.6	18.9	14.9

City	Ratio of Passing and Failing
A	7 : 3
B	5 : 3
C	4 : 5
D	1 : 3
E	3 : 2
F	7 : 5