Ratios and Proportions

To solve \(2:3 = x:6\), we use the property of proportions: \(2 \times 6 = 3 \times x\), which simplifies to \(x = 4\).

The ratio \(4:16\) simplifies to \(1:4\) by dividing both terms by 4.

The ratio of red balls to blue balls is \(6:9\), which simplifies to \(2:3\).

The ratio of 10 to 20 is \(1:2\).

To find \(x:z\), we combine the ratios \(x:y = 4:5\) and \(y:z = 2:3\).

First, make the y terms equal: \(x:y:z = 8:10:15\), so \(x:z = 8:15\).

To find the fourth proportional, set up the proportion \(3:9 = 12:x\).

Solving for \(x\) gives \(x = 36/3 = 24\).

50 paise is to Rs. 5 as \(0.5:5\), which simplifies to \(1:10\).

If the larger part is 40 in the ratio \(3:5\), then the smaller part is \(\frac{3}{5} \times 40 = 24\).

If 4 pencils cost Rs. 12, then each pencil costs Rs. 3.

Therefore, 10 pencils will cost \(10 \times 3 = Rs. 30\).

To solve \(3:x = 6:8\), we use the property of proportions: \(3 \times 8 = 6 \times x\), which simplifies to \(x = 4\).

1 hour is 60 minutes, so the ratio of 60 minutes to 45 minutes is \(60:45\), which simplifies to \(4:3\).

If the ratio of boys to girls is \(5:6\) and there are 30 boys, then the number of girls is \(\frac{6}{5} \times 30 = 36\).

If 16 men can complete a job in 10 days, then 8 men will take twice as long, which is 20 days.

To solve \(x:9 = 4:6\), we use the property of proportions: \(x \times 6 = 9 \times 4\), which simplifies to \(x = 6\).

The ratio \(24:36\) simplifies to \(2:3\) by dividing both terms by 12.

If the ratio of two numbers is \(3:4\) and their sum is 35, then the larger number is \(\frac{4}{7} \times 35 = 20\).