Ratio and Proportion

Divide 100 into two parts such that they are proportional to 3:5.

• 63,37

• 37.5,62.5

• 38,62

• 40,60

Answer explanation

Let's the value of two parts are 3k and 5k, where k is a constant.Since the total sum of two parts is 100, we can write,

3k + 5k = 100

8k = 100

k = 12.5

So, the parts are

3k = 3 × 12.5 = 37.5 &

5k = 5 × 12.5 = 62.5

If a: b = 5: 9 and b: c = 7: 4, then find a: b: c.

• 35:63:35

• 35:63:36

• 35:62:36

• 45:60:40

Answer explanation

Here, we make the common term ‘b’ equal in both ratios.

Therefore, we multiply the first ratio by 7 and the second ratio by 9.

So, we have a : b = 35 : 63 and b : c = 63 : 36

Thus, a : b : c = 35 : 63 : 36

In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is

• 550

• 416

• 300

• 200

Answer explanation

Let the number of boys and girls be 8x and 5x.

As we know number of girls is 160.

We even know 5x is the ratio of girls in the college.

Therefore, 5x =160 => x = 32

Total number of students = 8x + 5x = 13x

Total number of students = 13 * 32 = 416

Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

• 22:1

• 22:4

• 24:3

• 25:2

Answer explanation

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.

US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.

Now US : Indian = 25 : 10, and Indian : British = 10 : 2

Hence the two ratios can be combined and US : British = 25 : 2

In a zoo, there are rabbits and pigeons. If heads are counted, there are 340 heads and if legs are counted there are 1060 legs.How many pigeons are there?

• 150

• 160

• 180

• 190

Answer explanation

Suppose there are all the pigeons then total no of heads are 340 and total no of legs are 1060. Let us suppose number of rabbits is x and number of pigeons is y.

We know rabbit has 4 legs and pigeon has 2.

so, 1st equation will be x + y = 340

and, 2nd equation will be 4x + 2y = 1060.

solving, 1st and 2nd equation we get number of pigeons = 150

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

• 2:5

• 3:5

• 4:5

• 6:7

Answer explanation

The ratio between two numbers is 2 : 11. If the difference between the numbers is 81 find the smaller number.

• 10

• 12

• 18

• 16

Answer explanation

Quantity of milk= (60×23)litres = 40litres

 Quantity of water in it = (60−40) litres = 20 litres

New ratio = 1 : 2

Let quantity of water to be added further be x litre

Let the ratio be in terms of x.

The first number = 2x

The second number = 11x

The difference between the numbers = 11x – 2x = 9x

9x = 81

2x = 81 / 9 * 2 = 18

The ratio of two numbers is 11 : 12. If the sum of the numbers is 253, find the difference between the numbers.

• 10

• 11

• 12

• 21

Answer explanation

Let the ratio of the numbers be in terms of x.

The sum of the numbers = 11x + 12x = 23x

The sum of the numbers = 23x = 253

The difference between the numbers = 12x – 11x = x

X = 253 / 23 = 11

The product of two numbers is 693. If the numbers are in a ratio 7 : 11, find the difference between the numbers.

• 10

• 12

• 14

• 16

Answer explanation

Let the ratios be in terms of x.

The numbers will be 7x and 11x.

The product of the numbers = 7x * 11x = 77x2 = 693

X2 = 693 / 77 = 9

X = 3

The numbers = 7x, 11x = 21, 33

The difference between the numbers = 33 – 21 = 12

Three numbers are in a ratio 8 : 9 : 10. Which of the following can be a sum of the numbers?

• 2592

• 2593

• 2590

• 2582

Answer explanation

The only possible sum of the numbers can be any digit which is a multiple of 27.

The sum of the terms of the ratio is 27 that means that the sum of the digits will be a multiple of 27 with x being the constant. Thus, the digits must be a multiple of 27. The only option multiple of 27 is 2592.