Practice | Hashtable

31. Study the following pie-chart and the table given below it carefully to answer the questions given below:
Percentage-wise distribution of lecturers in 6 different subjects in a total number of lecturers: 1600.

Ratio of male to female lecturers

Lecturers Males : Females

Mathematics 3 : 4

Education 5 : 3

Hindi 1 : 3

Chemistry 1 : 7

Physics 9 : 5

Zoology 7 : 9

Total number of lecturers (both male and female) in Hindi is approximately what percent of the total number of female lecturers in Mathematics and chemistry together?

A. 58%

B. 43%

C. 47%

D. 51%

Discuss

Solution:

Number of lecturers in various subjects are:

\begin{aligned} Chemistry → \frac{13}{100} \times 1600 = 208 \\ Education → \frac{18}{100} \times 1600 = 288 \\ Hindi → \frac{12}{100} \times 1600 = 192 \\ Mathematics → \frac{21}{100} \times 1600 = 336 \\ Physics → \frac{14}{100} \times 1600 = 224 \\ Zoology → \frac{22}{100} \times 1600 = 352 \end{aligned}

Subject	Number of Males	Number of Females
Chemistry	208 × $\frac{1}{8}$ = 26	208 - 26 = 182
Education	288 × $\frac{5}{8}$ = 180	288 - 180 = 108
Hindi	192 × $\frac{1}{4}$ = 48	192 - 48 = 144
Mathematics	336 × $\frac{3}{7}$ = 144	336 - 144 = 192
Physics	224 × $\frac{9}{14}$ = 144	224 - 144 = 80
Zoology	352 × $\frac{7}{16}$ = 154	352 - 154 = 198

\begin{aligned} Required % \\ = (\frac{192}{192 + 182} \times 100) % \\ = (\frac{192}{374} \times 100) % \\ = \frac{9600}{187} % \\ = 51.3 % \\ \approx 51 % \end{aligned}

32. Study the following pie-chart and the table given below it carefully to answer the questions given below:
Percentage-wise distribution of lecturers in 6 different subjects in a total number of lecturers: 1600.

Ratio of male to female lecturers

Lecturers Males : Females

Mathematics 3 : 4

Education 5 : 3

Hindi 1 : 3

Chemistry 1 : 7

Physics 9 : 5

Zoology 7 : 9

What is the difference between the number of female lecturers in Zoology and the number of male lecturers in Hindi?

A. 156

B. 160

C. 150

D. 153

Discuss

Solution:

Number of lecturers in various subjects are:

\begin{aligned} Chemistry → \frac{13}{100} \times 1600 = 208 \\ Education → \frac{18}{100} \times 1600 = 288 \\ Hindi → \frac{12}{100} \times 1600 = 192 \\ Mathematics → \frac{21}{100} \times 1600 = 336 \\ Physics → \frac{14}{100} \times 1600 = 224 \\ Zoology → \frac{22}{100} \times 1600 = 352 \end{aligned}

Subject	Number of Males	Number of Females
Chemistry	208 × $\frac{1}{8}$ = 26	208 - 26 = 182
Education	288 × $\frac{5}{8}$ = 180	288 - 180 = 108
Hindi	192 × $\frac{1}{4}$ = 48	192 - 48 = 144
Mathematics	336 × $\frac{3}{7}$ = 144	336 - 144 = 192
Physics	224 × $\frac{9}{14}$ = 144	224 - 144 = 80
Zoology	352 × $\frac{7}{16}$ = 154	352 - 154 = 198

Required difference
= 198 - 48
= 150

33. Study the following pie-chart and the table given below it carefully to answer the questions given below:
Percentage-wise distribution of lecturers in 6 different subjects in a total number of lecturers: 1600.

Ratio of male to female lecturers

Lecturers Males : Females

Mathematics 3 : 4

Education 5 : 3

Hindi 1 : 3

Chemistry 1 : 7

Physics 9 : 5

Zoology 7 : 9

What is the ratio of the number of female lecturers in Physics to the number of male lecturers in Mathematics?

A. 5 : 9

B. 2 : 9

C. 3 : 7

D. 5 : 3

Discuss

Solution:

Number of lecturers in various subjects are:

\begin{aligned} Chemistry → \frac{13}{100} \times 1600 = 208 \\ Education → \frac{18}{100} \times 1600 = 288 \\ Hindi → \frac{12}{100} \times 1600 = 192 \\ Mathematics → \frac{21}{100} \times 1600 = 336 \\ Physics → \frac{14}{100} \times 1600 = 224 \\ Zoology → \frac{22}{100} \times 1600 = 352 \end{aligned}

Subject	Number of Males	Number of Females
Chemistry	208 × $\frac{1}{8}$ = 26	208 - 26 = 182
Education	288 × $\frac{5}{8}$ = 180	288 - 180 = 108
Hindi	192 × $\frac{1}{4}$ = 48	192 - 48 = 144
Mathematics	336 × $\frac{3}{7}$ = 144	336 - 144 = 192
Physics	224 × $\frac{9}{14}$ = 144	224 - 144 = 80
Zoology	352 × $\frac{7}{16}$ = 154	352 - 154 = 198

Required ratio
= 80 : 144
= 5 : 9

34. Study the following pie-chart carefully and answer the questions given below:
Cost Estimated by a Family in Renovation of their House.

What is the cost estimated by the family on painting and flooring together?

A. Rs. 36500

B. Rs. 34800

C. Rs. 36000

D. Rs. 34500

Discuss

Solution:

Cost estimated on painting and flooring together

\begin{aligned} = Rs. \frac{15 + 14}{100} \times 120000 \\ = Rs. \frac{29}{100} \times 120000 \\ = Rs. 34800 \end{aligned}

35. Study the following pie-chart carefully and answer the questions given below:
Cost Estimated by a Family in Renovation of their House.

What is the difference in the amount estimated by the family on interior decoration and that on architect’s fee?

A. 10000

B. 9500

C. 7200

D. 9000

Discuss

Solution:

\begin{aligned} Required Difference \\ = Rs. \frac{19 - 11}{100} \times 120000 \\ = Rs. \frac{8}{100} \times 120000 \\ = Rs. 9600 \end{aligned}

36. Study the following pie-chart carefully and answer the questions given below:
Cost Estimated by a Family in Renovation of their House.

The family gets a discount on furniture and pays 12% less than the estimated cost on furniture. What is the amount spent on furniture?

A. Rs.13200

B. Rs. 14526

C. Rs. 13526

D. Rs. 13728

Discuss

Solution:

\begin{aligned} Amount spent on furniture \\ = Rs. \frac{88}{100} \times \frac{13}{100} \times 120000 \\ = Rs. 13728 \end{aligned}

37. Study the following pie-chart carefully and answer the questions given below:
Cost Estimated by a Family in Renovation of their House.

Other than getting the discount of 12% on the estimated cost of furniture and actual miscellaneous expenditure being Rs. 10200 instead of the estimated one, the family's estimated cost is correct. What is the total amount spent by the family in renovating its house?

A. Rs. 116728

B. Rs. 115926

C. Rs. 119500

D. Rs. 116500

Discuss

Solution:

Estimated cost of furniture and miscellaneous expenditure

\begin{aligned} = Rs. \frac{13 + 8}{100} \times 120000 \\ = Rs. \frac{21}{100} \times 120000 \\ = Rs. 25200 \\ Actual cost of furniture \\ = Rs. \frac{88}{100} \times \frac{13}{100} \times 120000 \\ = Rs. 13728 \end{aligned}

Actual cost of furniture and miscellaneous expenditure
= Rs. (13728 + 10200)
= Rs. 23928
Total amount spent in renovating the house
= Rs. (120000 - 25200 + 23928)
= Rs. 118728

38. Study the following pie-chart and table carefully and answer the questions given below:
Percentage-wise Distribution of the Number of Mobile phones Sold by a Shopkeeper During Six Months. Ratio of mobile phones sold of Company A & Company B.

Total number if mobile phones sold = 45000

Month Ratio (A : B)

July 8 : 7

August 4 : 5

September 3 : 2

October 7 : 5

November 7 : 8

December 7 : 9

If the shopkeeper earned a profit of Rs. 433 on each mobile phone sold of company B during October, what was his total profit earned on the mobile phones of that company during the same month?

A. Rs. 649900

B. Rs. 645900

C. Rs. 649400

D. Rs. 649500

Discuss

Solution:

Number of mobile phones sold by B during October

\begin{aligned} = 45000 \times \frac{8}{100} \times \frac{5}{12} \\ = 1500 \\ ∴ Required profit \\ = Rs. (1500 \times 433) \\ = Rs. 649500 \end{aligned}

39. Study the following pie-chart and table carefully and answer the questions given below:
Percentage-wise Distribution of the Number of Mobile phones Sold by a Shopkeeper During Six Months. Ratio of mobile phones sold of Company A & Company B.

Total number if mobile phones sold = 45000

Month Ratio (A : B)

July 8 : 7

August 4 : 5

September 3 : 2

October 7 : 5

November 7 : 8

December 7 : 9

What is the ratio of the number of mobile phones sold of company B during July to those sold during December of the same company?

A. 119 : 145

B. 116 : 135

C. 119 : 135

D. 119 : 130

Discuss

Solution:

Number of mobile phones sold by B during July

\begin{aligned} = 45000 \times \frac{17}{100} \times \frac{7}{15} \\ = 3570 \end{aligned}

Number of mobile phones sold by B during December

\begin{aligned} = 45000 \times \frac{16}{100} \times \frac{9}{16} \\ = 4050 \\ ∴ Required ratio \\ = \frac{3570}{4050} \\ = \frac{119}{135} \\ = 119 : 135 \end{aligned}

40. Study the following pie-chart and table carefully and answer the questions given below:
Percentage-wise Distribution of the Number of Mobile phones Sold by a Shopkeeper During Six Months. Ratio of mobile phones sold of Company A & Company B.

Total number if mobile phones sold = 45000

Month Ratio (A : B)

July 8 : 7

August 4 : 5

September 3 : 2

October 7 : 5

November 7 : 8

December 7 : 9

The number of mobile phones sold of Company A during July is approximately what percent of the number of mobile phones sold of company A during December?

A. 110%

B. 140%

C. 150%

D. 105%

Discuss

Solution:

Number of mobile phones sold by A during July

\begin{aligned} = 45000 \times \frac{17}{100} \times \frac{8}{15} \\ = 4080 \end{aligned}

Number of mobile phones sold by A during December

\begin{aligned} = 45000 \times \frac{16}{100} \times \frac{7}{16} \\ = 3150 \\ Let 4080 = x % of 3150 \\ Then, \\ \frac{x}{100} \times 3150 = 4080 \\ \Rightarrow x = \frac{4080 \times 2}{63} \\ \Rightarrow x = 129.5 \\ \Rightarrow x \approx 130 \\ Required percentage  = 130% \end{aligned}

Lecturers	Males : Females
Mathematics	3 : 4
Education	5 : 3
Hindi	1 : 3
Chemistry	1 : 7
Physics	9 : 5
Zoology	7 : 9

Total number if mobile phones sold = 45000
Month	Ratio (A : B)
July	8 : 7
August	4 : 5
September	3 : 2
October	7 : 5
November	7 : 8
December	7 : 9