Ratio and Proportion

(46) The ratio of the number of boys to girls in a school is 3:4. If there are 120 girls in the school, how many boys are there?

• (a) 90 boys
• (b) 90 boys
• (c) 80 boys
• (d) 100 boys

Answer

Correct Answer: (b) 90 boys
Let the number of boys in the school be \(3x\) and the number of girls be \(4x\).
According to the problem, we have:
\[\frac{3x}{4x} = \frac{B}{120}\]
Cross-multiplying gives us:
\[3x \cdot 120 = 4x \cdot B\]
\[360x = 4x \cdot B\]
Dividing both sides by \(4x\) (since \(x\) cannot be zero), we get:
\[B = \frac{360x}{4x}\]
\[B = 90\]
So, the number of boys in the school is \(3x = 3 \cdot 30 = 90\).
Therefore, there are 90 boys in the school.

(47) The ratio of the lengths of two ropes is 2:5. If the shorter rope is 10 meters long, how long is the longer rope?

• (a) 15 meters
• (b) 25 meters
• (c) 20 meters
• (d) 25 meters

Answer

Correct Answer: (d) 25 meters
Let the length of the longer rope be \(5x\) meters.
According to the problem, we have:
\[\frac{10}{5x} = \frac{2}{5}\]
Cross-multiplying gives us:
\[10 \cdot 5 = 2 \cdot 5x\]
\[50 = 10x\]
\[x = \frac{50}{10}\]
\[x = 5\]
So, the length of the longer rope is \(5x = 5 \cdot 5 = 25\) meters.
Therefore, the longer rope is 25 meters long.

(48) A recipe calls for a mixture of sugar and flour in the ratio of 3:7. If the recipe requires 420 grams of sugar, how many grams of flour are needed?

• (a) 980 grams
• (b) 560 grams
• (c) 980 grams
• (d) 140 grams

Answer

Correct Answer: (c) 980 grams
Let the amount of flour needed be \(7x\) grams.
According to the problem, we have:
\[\frac{3}{7} = \frac{420}{F}\]
Cross-multiplying gives us:
\[3 \cdot F = 7 \cdot 420\]
\[3F = 2940\]
\[F = \frac{2940}{3}\]
\[F = 980\]
So, the amount of flour needed is \(7x = 7 \cdot 140 = 980\) grams.
Therefore, 980 grams of flour are needed.

(49) The ratio of the number of apples to oranges in a fruit basket is 5:3. If there are 24 oranges in the basket, how many apples are there?

• (a) 24 apples
• (b) 30 apples
• (c) 40 apples
• (d) 20 apples

Answer

Correct Answer: (c) 40 apples
Let the number of apples in the basket be \(5x\) and the number of oranges be \(3x\).
According to the problem, we have:
\[\frac{5x}{3x} = \frac{A}{24}\]
Cross-multiplying gives us:
\[5x \cdot 24 = 3x \cdot A\]
\[120x = 3x \cdot A\]
Dividing both sides by \(3x\) (since \(x\) cannot be zero), we get:
\[A = \frac{120x}{3x}\]
\[A = 40\]
So, the number of apples in the basket is \(5x = 5 \cdot 8 = 40\).
Therefore, there are 40 apples in the basket.

(50) The ratio of the areas of two similar squares is 4:9. If the area of the smaller square is 36 square meters, what is the area of the larger square?

• (a) 121 square meters
• (b) 81 square meters
• (c) 100 square meters
• (d) 81 square meters

Answer

Correct Answer: (d) 81 square meters
Let the area of the larger square be \(9x\) square meters.
According to the problem, we have:
\[\frac{36}{9x} = \frac{4}{9}\]
Cross-multiplying gives us:
\[36 \cdot 9 = 4 \cdot 9x\]
\[324 = 36x\]
\[x = \frac{324}{36}\]
\[x = 9\]
So, the area of the larger square is \(9x = 9 \cdot 9 = 81\) square meters.
Therefore, the area of the larger square is 81 square meters.