Find the difference between the average number of beaches in D, E and C and the average number of mountains in B, A and E.

Read the following bar graph and table carefully and answer the questions given below. The bar graph shows total number of beaches in five different countries. The table shows percentage of mountains out of total beaches and mountains together in these countries.

Countries	Percentage of mountains out of total beaches and mountains together
A	60%
B	75%
C	20%
D	80%
E	50%

The correct answer is 40.

From the provided bar graph, we can observe the total number of beaches in each country:

• Country A = 100
• Country B = 80
• Country C = 120
• Country D = 150
• Country E = 60

Let $M$ represent the number of mountains and $B$ represent the number of beaches in a country. The percentage of mountains out of the total beaches and mountains together is given by:

$\text{Percentage of mountains}=\frac{M}{M+B}\times 100$

Rearranging this formula, we can calculate the number of mountains ($M$) directly using the number of beaches ($B$):

$M=\frac{\text{Percentage of mountains}}{100-\text{Percentage of mountains}}\times B$

Now, let us find the number of mountains in countries B, A, and E:

1. Country B:
Percentage of mountains = 75%
$M_{\text{B}}=\frac{75}{100-75}\times 80=\frac{75}{25}\times 80=3\times 80=240$

2. Country A:
Percentage of mountains = 60%
$M_{\text{A}}=\frac{60}{100-60}\times 100=\frac{60}{40}\times 100=1.5\times 100=150$

3. Country E:
Percentage of mountains = 50%
$M_{\text{E}}=\frac{50}{100-50}\times 60=\frac{50}{50}\times 60=1\times 60=60$

Now, calculate the required averages:

Average number of beaches in D, E, and C:
$\text{Average beaches}=\frac{150+60+120}{3}=\frac{330}{3}=110$

Average number of mountains in B, A, and E:
$\text{Average mountains}=\frac{240+150+60}{3}=\frac{450}{3}=150$

Finally, calculate the difference between the two averages:

$\text{Difference}=150-110=40$