Find the ratio of total private projects handled in Q-3 and Q-4 together to Government projects handled in Q-1 and Q-2 together.

The graph given below shows the percentage distribution of total number projects (private + public) handled in 4 quarters Q-1, Q-2, Q-3 and Q-4 in years 2022. The table shows the percentage of private projects handled wrt projects handled in respective quarters and number of government projects. Read the pie chart and table carefully and answer the following questions.

Quarters	Percentage of private projects	Number of government projects
Q-1	50	300
Q-2	60	160
Q-3	40	420
Q-4	30	210

The correct answer is 37:46.

Step 1: Understand the given data from the pie chart and the table.
The pie chart displays the percentage distribution of total projects (Private + Government) across four quarters:
- 1^st Quarter (Q-1) = 30%
- 2^nd Quarter (Q-2) = 20%
- 3^rd Quarter (Q-3) = 35%
- 4^th Quarter (Q-4) = 15%

The table provides the percentage of private projects and the number of government projects for each quarter:
- Q-1: 50% Private projects, 300 Government projects
- Q-2: 60% Private projects, 160 Government projects
- Q-3: 40% Private projects, 420 Government projects
- Q-4: 30% Private projects, 210 Government projects

Step 2: Calculate the total number of projects in each quarter.
Since the total projects in any quarter is the sum of Private and Government projects, we can calculate the total projects from the percentage of government projects (which is $100\%-\text{Percentage of Private projects}$).

- For Q-1:
Percentage of Government projects = $100\%-50\%=50\%$
Since 50% of the projects correspond to 300 government projects:
Total projects in Q-1 = $\frac{300}{0.50}=600$

- For Q-2:
Percentage of Government projects = $100\%-60\%=40\%$
Since 40% of the projects correspond to 160 government projects:
Total projects in Q-2 = $\frac{160}{0.40}=400$

- For Q-3:
Percentage of Government projects = $100\%-40\%=60\%$
Since 60% of the projects correspond to 420 government projects:
Total projects in Q-3 = $\frac{420}{0.60}=700$

- For Q-4:
Percentage of Government projects = $100\%-30\%=70\%$
Since 70% of the projects correspond to 210 government projects:
Total projects in Q-4 = $\frac{210}{0.70}=300$

Step 3: Calculate the total private projects handled in Q-3 and Q-4 together.
- Private projects in Q-3 = $40\%\text{of}700=0.40\times 700=280$
- Private projects in Q-4 = $30\%\text{of}300=0.30\times 300=90$
Total Private projects in (Q-3 + Q-4) = $280+90=370$

Step 4: Calculate the total Government projects handled in Q-1 and Q-2 together.
- Government projects in Q-1 = 300
- Government projects in Q-2 = 160
Total Government projects in (Q-1 + Q-2) = $300+160=460$

Step 5: Find the required ratio.
Ratio = $370:460=37:46$