RATIO AND PROPORTION PRACTICE QUESTIONS FOR CA FIUNDATION

Problem 1 :

The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. Find the age of the youngest boy.

Solution:

Total age of 3 boys = (25 × 3) years 

= 75 years

Ratio of their ages = 3 : 5 : 7

Age of the youngest = (75 × 3/15)

= 15 years

So, the age of the youngest boy is 15 years.

Problem 2 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Solution:

Ratio of angles = 2 : 7 : 11

Let the angles of a triangle be 2x, 7x, 11x.

Sum of three angles of a triangle is 180 degree.

2x + 7x + 11x = 180

20x = 180

x = 9

So, the angles are,

2x = 2(9) = 18°

7x = 7(9)= 63°

11x = 11(9) = 99°

Problem 3 :

Two numbers are respectively 20% and 50% are more than a third number, Find the ratio of the two numbers.

Solution:

Let the third number be x.

Thus, the ratio of two number is 4 : 5.

Problem 4 :

If $782 is divided among three persons A, B and C in the ratio 1/2 : 2/3 : 3/4, then find the share of A.

Solution:

Given, number = 782

So, share of A is $204.

Problem 5 :

An amount of money is to be divided among P, Q and R in the ratio 3 : 7 : 12. The difference between the shares of P and Q is $2400. What will be the difference the shares of Q and R?

Solution:

The ratio of P, Q and R is 3 : 7 : 12.

Let x be the amount of money share.

Ratio = 3x : 7x : 12x

The sum of ratios = 22x

7x - 3x = 2400

4x = 2400

x = 600

The share difference between Q and R = 12x - 7x = 5x

= 5 × 600

= 3000

The share difference between Q and R is $3000.

Problem 6 :

Carter's SUV requires 8 gallons of gasoline to travel 148 miles. How many gasoline, to the nearest gallon, will he need for 500 mile trip?

Solution:

Let x be the quantity off gasoline in gallons.

8 : 148 = x : 500

product of extremes = Product of means

8 ⋅ 500 = 148 ⋅ x

x = (4000/148)

x = 27.02

So, Carter needs 27.02 gallons of gasoline for a 500 mile trip.

Problem 7 :

If 5x : 3 = (x + 14) : 2, what is the value of x?

Solution:

So, the value of x is 6.

Problem 8 :

If 15 people can repair a road of length 150 meters, at the same rate, how many people are needed to repair a road of length 420 meters.

Solution:

The ratio between number of people and length of road repaired is

= 15 : 150

= 1 : 10 --- (1)

Let x be the number of people needed to repair a road of length 420 meters.

Then, 

x : 420 --- (2)

From (1) and (2),

1 : 10 = x : 420

1(420) = 10(x)

420 = 10x

Divide each side by 10.

x = 42

So, 42 people are needed to repair a road of length 420 meters.

Problem 9 :

John weighs 56.7 kilograms. If he is going to reduce his weight in the ratio 7 : 6, find his new weight.

Solution:

Let the previous weight be 7x.

7x = 56.7

x = 8.1

Therefore, the new weight = 6 × 8.1

= 48.6 kg

Problem 10 :

If a : b = c : d = 2.5 : 1.5, what are the values of ad : bc and a + c : b + d?

Solution:

In the given proportion a : b and c : d, applying cross product rule, we get

ad = bc

Dividing by bc on both sides, we get

ad : bc = 1 : 1

Given: a : b = c : d = 2.5 : 1.5 --- (1)

In the given proportion a : b and c : d, applying the property addendo, we get 

a : b = c : d = (a + b) : (c + d) --- (2)

From (1) and (2), we get

(a + b) : (c + d) = 2.5 : 1.5

(a + b) : (c + d) = (2.5 × 10) : (1.5 × 10)

 (a + b) : (c + d) = 25 : 15