Ratio and Proportion III

The ratio of Math to Science books is 2:3 while the ratio of Science to English books is 4:5. If there are 150 English books, how many Math books are there?

• 80

• 90

• 100

• 120

Answer explanation

Since there are 150 English books and the ratio of Science to English books is 4:5, there are 120 Science books. Given the Math to Science ratio is 2:3, there are 80 Math books (2/3 * 120). Therefore, there are 80 Math books.

If the ratio of apples to oranges is 3:4 and there are 120 oranges, how many apples are there?

• 60

• 80

• 90

• 100

Answer explanation

Since the ratio of apples to oranges is 3:4, for every 4 parts there are 120 oranges, so 1 part is 30 oranges. Therefore, there are 3 parts of apples, which is 3 * 30 = 90 apples.

A bakery sells cakes and cookies in the ratio of 5:3. If there are 80 cookies, how many cakes are there?

• 40

• 50

• 60

• 70

Answer explanation

To find the number of cakes, multiply the ratio by the number of cookies. 5:3 ratio means 5 parts cakes to 3 parts cookies. So, 80 cookies / 3 = 26.67, then 26.67 * 5 = 133.33 cakes. Since we can't have a fraction of a cake, the closest whole number is 60 cakes.

The ratio of boys to girls in a class is 2:3. If there are 90 girls, how many boys are there?

• 40

• 45

• 50

• 55

Answer explanation

Since the ratio of boys to girls is 2:3, for every 3 girls, there are 2 boys. With 90 girls, there are 90/3 = 30 sets of girls. Therefore, there are 30*2 = 60 boys in total, which means there are 60-90 = 30 more boys than girls. So, there are 90+30 = 120 boys in the class.

If the ratio of pens to pencils is 3:4 and there are 120 pencils, how many pens are there?

• 60

• 80

• 90

• 100

Answer explanation

Since the ratio of pens to pencils is 3:4, for every 4 pencils, there are 3 pens. With 120 pencils, there are 120/4 = 30 sets of 3 pens, totaling 30*3 = 90 pens.

The ratio of red marbles to blue marbles is 2:5. If there are 70 blue marbles, how many red marbles are there?

• 20

• 25

• 30

• 35

Answer explanation

Since the ratio of red marbles to blue marbles is 2:5, for every 5 blue marbles, there are 2 red marbles. Therefore, with 70 blue marbles, there are 2/5 * 70 = 28 red marbles.

In a bag, the ratio of green balls to yellow balls is 3:2. If there are 80 yellow balls, how many green balls are there?

• 90

• 100

• 120

• 150

Answer explanation

Since the ratio of green to yellow balls is 3:2, for every 2 yellow balls, there are 3 green balls. With 80 yellow balls, there are 120 green balls (80 yellow * 3 green / 2 yellow). Therefore, there are 120 green balls.

If the ratio of mangoes to apples is 2:3 and there are 120 apples, how many mangoes are there?

• 60

• 80

• 90

• 100

Answer explanation

If the ratio of mangoes to apples is 2:3, and there are 120 apples, then the total parts are 2+3=5. So, each part is 120/3=40. Therefore, the number of mangoes is 2*40=80.

In a box, the ratio of red balls to blue balls is 5:3. If there are 72 blue balls, how many red balls are there?

• 40

• 45

• 50

• 55

Answer explanation

Since the ratio of red to blue balls is 5:3, for every 3 blue balls, there are 5 red balls. With 72 blue balls, there are 120 red balls (5*24). Therefore, there are 120-72=48 more red balls than blue balls, making the total red balls 72+48=120.

If the ratio of shirts to pants is 3:4 and there are 160 pants, how many shirts are there?

• 90

• 120

• 150

• 180

Answer explanation

To find the number of shirts, multiply the number of pants (160) by the ratio of shirts to pants (3/4), giving 120 shirts.