Question

30. The bar graph given below shows the sales of books (in thousands) from six
branches of a publishing company during two consecutive years 2000 and 2001.

1. What is the ratio of the total sales of branch B2 for both years to the total ales of
branch B4 for both years?
2. What is the average sale of all the branches in thousand numbers) for the year
2000?
3. Total sales of branch B6 for both the years is what percent of the total sales of
branches B3 for both the years?​

Answer 1

$\tt{Solution \: \: (1):}$

The sales in branch 2 on the year 2000=75

The sales in branch 2 on the year 2001 =65

The total sales in branch 2 on both of these years:-

$= 75 + 65$

$=\bold{ 140}$

Thus, the total sales in branch 2 on both of these years=140

The sales in branch 4 on the year 2000=85

The sales in branch 4 on the year 2001 =95

The total sales in branch 2 on both of these years:-

$= 85 + 95$

$=\bold{ 180}$

Thus, the total sales in branch 4 on both of these years=180

The ratio of the sales in branch 2 to branch 4 on both these years :-

$= 140 : 180$

$= \frac{140}{180}$

$= \frac{140 \div 10}{180 \div 10}$

$= \frac{14}{18}$

$= \frac{14 \div 2}{18 \div 2}$

$= \frac{7}{9}$

$=\bold {7: 9}$

Thus, the ratio of the total sales in both these branches=7:9

Therefore, the ratio of the total sales in branch 2 to branch 4 in both of these consecutive years=7:9

$\tt{Solution \: \: (2) :}$

The sales in branch 1 in the year 2000=80

The sales in branch 2 in the year 2000=75

The sales in branch 3 in the year 2000=95

The sales in branch 4 in the year 2000=85

The sales in branch 5 in the year 2000=75

The sales in branch 6 in the year 2000=70

We know that :-

$\bold{average = \frac{sum \: of \: all \: values}{count \:of \: the \: values } }$

Which means, the average of the sales in all the branches on the year 2000:-

$= \frac{80 + 75 + 95 + 85 + 75 + 70}{6}$

$= \frac{480}{6}$

$= \bold{80}$

Thus, the average of the sales=80

Therefore, the average of the sales in all the branches during the year 2000=80

$\tt{Solution \: \: (3):}$

Sales in branch 6 in the year 2000=70

Sales in branch 6 in the year 2001=80

Total sales in branch 6 on both these years:-

$= 70 + 80$

$= \bold{150}$

Thus, the total sales in branch 6 in both of these years=150

Sales in branch 3 in the year 2000=95

Sales in branch 3 in the year 2001=110

Total sales made by branch 3 in both of these consecutive years:-

$=95 + 110$

$= \bold{205}$

Thus, the total sales made by branch 3 in the years 2000 and 2001=205

Total sales made by branch 6 as a percentage of total sales made by branch 3:-

Let x be the percentage.

Which means :-

$= x \: \% \: \: of \: \: 205 = 150$

$= \frac{x}{100} \times 205 = 150$

$= \frac{205x}{100} = 150$

$= 205x = 150 \times 100$

$= 205x = 15000$

$= x = \frac{15000}{205}$

$= x = 73.17$

Thus, the sales made by B6 as a percentage of sales made in B3=73.17%

Therefore, total sales made by branch 6 as a percentage of total sales made by branch 3=73.17%

Answer 2

Given:

A bar graph showing the sales of books (in thousands) from six branches of a publishing company during two consecutive years 2000 and 2001.

To find:

The answer to the above questions.

Solution:

The answers to the above questions are explained below:

1.

The sales of branch B2 in the year 2000 = 75

The sales of branch B2 in the year 2001 = 65

Thus, the total sales of branch B2 in both years (in thousand numbers) = S2 = 75 + 65 = 140.

Similarly,

The sales of branch B4 in the year 2000 = 85

The sales of branch B4 in the year 2000 = 95

Thus, the total sales of branch B4 in both years (in thousand numbers) = S4 = 85 + 95 = 180.

Hence, the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years =

$\frac{S2}{S4} = \frac{140}{180} = \frac{7}{9}$

Hence, the ratio of total sales of B2 and B4 for both the years is- 7:9.

2.

The average sale of all the branches in thousand numbers) for the year 2000 =

$\frac{total \: sales \: of \: all \: the \: branches \: for \: the \: year \: 2000}{number \: of \: branches}$

$= \frac{80 + 75 + 85 + 95 + 75 +70 }{6}$

$= \frac{480}{6}$

$= 80$

Hence, the average sale of all the branches (in thousand numbers) for the year 2000 is 80.

3.

Total sales of branch B6 for both the years = total

sales of branch B6 for the year 2000 + total

sales of branch B6 for the year 2001 = 70 + 80 = 150.

Similarly, total sales of branch B3 for both the years = 95 + 110 = 205.

Total sales made by branch B6 as a percentage of total sales made by branch B3 is

Let the percentage be x℅.

So,

$205 \times x\% = 150$

$205 \times \frac{x}{100} = 150$

$x = \frac{150 \times 100}{205} = \frac{3000}{41} \%$

$x = 73.17\%$

Hence, the total sales of branch B6 for both the years as a percentage of the total sales of branch B3 for both the years are- 73.17%.