Practice | Hashtable

21. Refer to the pie-chart and the table carefully and answer the given question.
Distribution of total number of cellular phones (both Nokia and Samsung) sold by six stores in October.

Ratio of the number of Nokia cellular phones sold to that of Samsung cellular phone sold.

Store Ratio

P 4 : 3

Q 3 : 1

R 5 : 4

S 7 : 6

T 1 : 4

U 11 : 10

What is the ratio of the number of Nokia cellular phones sold by store S to the Samsung cellular phones sold by store T and U together?

A. 43 : 72

B. 49 : 76

C. 43 : 76

D. 49 : 72

Discuss

Solution:

Store	Nokia Cellular Phones	Samsung Cellular Phones	Total Number of Cellular Phones
P	896	672	1568
Q	840	280	1120
R	1120	896	2016
S	1568	1344	2912
T	448	1792	2240
U	704	640	1344

Number of Nokia phones sold by store S = 1568
Number of Samsung Phones sold by store T and U together
= 1792 + 640
= 2432

\begin{aligned} ∴ Required ratio \\ = \frac{1568}{2432} \\ = \frac{49}{76} \\ = 49 : 76 \end{aligned}

22. Refer to the pie-chart and the table carefully and answer the given question.
Distribution of total number of cellular phones (both Nokia and Samsung) sold by six stores in October.

Ratio of the number of Nokia cellular phones sold to that of Samsung cellular phone sold.

Store Ratio

P 4 : 3

Q 3 : 1

R 5 : 4

S 7 : 6

T 1 : 4

U 11 : 10

The number of Nokia cellular phones sold by store R is what percent more than that of Samsung cellular phones sold by store P and Q together?

A. $23 \frac{1}{17}$ %

B. $19 \frac{5}{17}$ %

C. $18 \frac{3}{17}$ %

D. $17 \frac{11}{17}$ %

Discuss

Solution:

Store	Nokia Cellular Phones	Samsung Cellular Phones	Total Number of Cellular Phones
P	896	672	1568
Q	840	280	1120
R	1120	896	2016
S	1568	1344	2912
T	448	1792	2240
U	704	640	1344

Number of Nokia phones sold by store R = 1120
Number of Samsung phones sold by store P and Q together
= 672 + 280
= 952

\begin{aligned} ∴ Required percentage \\ = \frac{1120 - 952}{952} \times 100 \\ = \frac{16800}{952} % \\ = \frac{300}{17} % \\ = 17 \frac{11}{17} % more \end{aligned}

23. Refer to the pie-chart and the table carefully and answer the given question.
Distribution of total number of cellular phones (both Nokia and Samsung) sold by six stores in October.

Ratio of the number of Nokia cellular phones sold to that of Samsung cellular phone sold.

Store Ratio

P 4 : 3

Q 3 : 1

R 5 : 4

S 7 : 6

T 1 : 4

U 11 : 10

The total number of cellular phones (both Nokia and Samsung) sold by store Q increased by 15% from October to November and the same of cellular phones sold by store T increased by 5% from October to November. What was the total number of cellular phones sold by store Q and T together in November?

A. 3540

B. 3720

C. 3640

D. 3420

Discuss

Solution:

Store	Nokia Cellular Phones	Samsung Cellular Phones	Total Number of Cellular Phones
P	896	672	1568
Q	840	280	1120
R	1120	896	2016
S	1568	1344	2912
T	448	1792	2240
U	704	640	1344

Number of cellular phones (both Nokia and Samsung) sold by store Q in October
= 11200 ×

\frac{10}{100}

= 1120
∵ Number of cellular phones (both Nokia and Samsung) sold by store Q in November
= 1120 ×

\frac{115}{100}

= 1288
Number of cellular phones (both Nokia and Samsung) sold by store T in October
= 11200 ×

\frac{20}{100}

= 2240
∵ Number of cellular phones (both Nokia and Samsung) sold by store T in November
= 2240 ×

\frac{105}{100}

= 2352
∵ Total number of cellular phones (both Nokia and Samsung) sold by Q and T together in November
= 1288 + 2352
= 3640

24. Refer to the pie-chart and answer the given questions.
Distribution of total number of Dell Laptops Sold by 5 Stores.

Distribution of number of Laptops (both Dell and Lenovo) Sold by 5 Stores in 2011.

Number of Dell laptops sold by store Q is approximately what percent of the number of the number of laptops (both Dell and Lenovo) sold by store R?

A. 28%

B. 45%

C. 50%

D. 38%

Discuss

Solution:

Percent of Dell Laptops sold by store Q = 25%
Total number of Dell Laptops bold by store Q

\begin{aligned} = 2400 \times \frac{25}{100} \\ = 600 \end{aligned}

Percent of Laptops Dell and Lenovo sold by store R = 35%
Number of Laptops Dell and Lenovo sold by store R

\begin{aligned} = 4500 \times \frac{35}{100} \\ = 1575 \\ ∴ Required Percentage \\ = \frac{600}{1575} \times 100 \\ = 38.095 \\ \approx 38 % \end{aligned}

25. Refer to the pie-chart and answer the given questions.
Distribution of total number of Dell Laptops Sold by 5 Stores.

Distribution of number of Laptops (both Dell and Lenovo) Sold by 5 Stores in 2011.

Number of Dell laptops sold by store T is what percent more than the number of laptops sold by store P?

A. 30%

B. 45%

C. 40%

D. 42.5%

Discuss

Solution:

Number of Dell laptops sold by store T

\begin{aligned} = 2400 \times \frac{21}{100} \\ = 504 \end{aligned}

Number of Laptops sold by store P

\begin{aligned} = 2400 \times \frac{15}{100} \\ = 360 \end{aligned}

Required Percentage

\begin{aligned} = \frac{504 - 360}{360} \times 100 \\ = 40 % \end{aligned}

26. Refer to the pie-chart and answer the given questions.
Distribution of total number of Dell Laptops Sold by 5 Stores.

Distribution of number of Laptops (both Dell and Lenovo) Sold by 5 Stores in 2011.

What is the average number of Dell Laptops sold by stores, P R and S together?

A. 424

B. 432

C. 428

D. 454

Discuss

Solution:

Percent of Dell Laptops sold by P, R and S together
= 15% + 30% + 9%
= 54%
Total Dell Laptops sold by P, R and S together

\begin{aligned} = 2400 \times \frac{54}{100} \\ = 1296 \\ ∴ Average \\ = \frac{1296}{3} \\ = 432 \end{aligned}

27. Refer to the pie-chart and answer the given questions.
Distribution of total number of Dell Laptops Sold by 5 Stores.

Distribution of number of Laptops (both Dell and Lenovo) Sold by 5 Stores in 2011.

What is the difference between number of laptops (both Dell and Lenovo) sold by store Q and total number of Lenovo laptops sold by store R and S together?

A. 185

B. 99

C. 91

D. 119

Discuss

Solution:

Percent of Laptops Dell and Lenovo sold by store Q = 23%
Number of Laptops Dell and Lenovo sold by store Q

\begin{aligned} = 4500 \times \frac{23}{100} \\ = 45 \times 23 \\ = 1035 \end{aligned}

Percent of Laptops Dell and Lenovo sold by R and S together
= 35% + 11%
= 46%
Now, total number of Laptops Lenovo and Dell sold by R and S together

\begin{aligned} = 4500 \times \frac{46}{100} \\ = 2070 \end{aligned}

Percent of Dell Laptops sold by R and S together
= 30% + 9%
= 39%
Number of Dell Laptops sold by R and S together

\begin{aligned} = 2400 \times \frac{39}{100} \\ = 936 \end{aligned}

Number of Lenovo Laptops = 2070 - 936 = 1134
Required difference
= 1134 - 1035
= 99

28. Refer to the pie-chart and answer the given questions.
Distribution of total number of Dell Laptops Sold by 5 Stores.

Distribution of number of Laptops (both Dell and Lenovo) Sold by 5 Stores in 2011.

What is the central angle corresponding to number of Dell laptops sold by store S?

A. 29.4°

B. 38.6°

C. 36.2°

D. 32.4°

Discuss

Solution:

Dell laptops sold by store S = 9%
Central angle corresponding to number of Dell Laptops sold by store S

\begin{aligned} = \frac{9}{100} \times 360 \\ = 32.4 ° \end{aligned}

29. 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 total number of lecturers (both male and female) is Zoology and the total number of male lecturers in Chemistry and Education Together?

A. 192

B. 182

C. 146

D. 136

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
= 352 - (26 + 180)
= 352 - 206
= 146

30. 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 total number of male lecturers in the university?

A. 696

B. 702

C. 712

D. 668

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

Total number of male lecturers in the university
= 26 + 180 + 48 + 144 + 144 + 154
= 696

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