RATIO AND PROPORTION PRACTICE FOR SAT

Problem 1 :

The number of lollipops. Sam gets on her birthday varies directly with her age. If Sam got 15 lollipops when she was 6 years old, how many lollipops will she get when Sam is 18 years old ?

Solution :

Number of lollipops she gets = 15 lollipops

When he age is 6.

Let x be the number of lollipops, he gets 18 years old.

6 : 15 = 18 : x

6/15 = 18/x

6x = 18(15)

x = 18(15)/6

x = 3(15)

x = 45 lollipops

Problem 2 :

How many toys parts can a machine make in 10 minutes, if this machine can make 36 toy parts in 1 hour ?

Solution :

In 1 hour, it can make 36 toy parts.

Let x be the number of toys can be made in 10 minutes.

Let us convert both into minutes.

1 hour = 60 minutes

60 : 36 = 10 : x

60/36 = 10/x

60x = 36(10)

x = 360/60

x = 10

So, a machine can make 10 toys.

Problem 3 :

If a small dog can run 12 miles in 1.5 hours and a mountain cat can travel twice as fair in half the time, what was mountain cat's speed, in miles per hour ?

Solution :

Distance covered by the dog in 1.5 hours = 12 miles

Distance covered by the cat in 1.5/2 (or) 0.75 hours = 12(2)

= 24 miles

Let x be the required distance covered by the cat per hour.

0.75 : 24 = 1 : x

0.75/24 = 1/x

0.75x = 24

x = 24/0.75

x = 32 miles.

So, the distance covered by the cat in one hour is 32 miles.

Problem 4 :

A Jaguar can run at speeds up to 70 miles per hour. About how many miles can a Jaguar run in 5 seconds ?

Solution :

Distance covered by Jaguar in one hour = 70 miles

1 : 70

Converting hours to minutes, 1 hour = 60 minute

1 minute = 60 seconds

1 hour = 3600 seconds

Let x be the required distance,

3600 : 70 = 5 : x

3600/70 = 5/x

x = 5(70)/3600

x = 0.097

Approximately 0.1 miles is the required distance.

Problem 5 :

For a certain type of heater, the increase in gas bills is directly proportional to the temperature setting (in Fahrenheit). If the gas bills increased by $20 when the temperature setting is increased by 4 degrees. Fahrenheit, by how much will expenses increase when the temperature setting is increased by 10 Fahrenheit ?

Solution :

Let x be the required increases.

20 : 4 = x : 10

20/4 = x /10

5 = x / 10

x = 50

So, the answer is 50.

Problem 6 :

Kim spent 2.5 hours installing 700 square feet of solar panels. At this rate, how many hours will she required to install 4200 square feet of solar panels.

Solution :

Number of hours Kim is working = 2.5 hours

Number of square feet of solar panels = 700

Let x be the number of hours she requires.

2.5 : 700 = x : 4200

2.5/700 = x/4200

2.5(4200) = 700x

x = 2.5(4200)/700

x = 15

So, the required number of hours is 15.

Problem 7 :

A worker can complete the assembly of 10 toys in 20 minutes. At the same rate, how many minutes does he need to assemble 20 toys ?

Solution :

Let x be the required number of minutes.

Time taken = 20 minutes

Number of toys assembled = 10

20 : 10 = x : 20

20/10 = x/20

400 = 10x

x = 400/10

x = 40 minutes.