# Dividing a Quantity in a given Ratio

We will follow the rules of dividing a quantity in a given ratio (two or three) to solve different types of problems.

1. 20 apples are distributed between Aaron and Ben in the ratio 2 : 3. Find, how many does each get?

Solution:

Aaron and Ben get apples in the ratio 2 : 3 i.e. if Aaron gets 2 parts, B should get 3 parts.

In other words, if we make (2 + 3) = 5 equal parts, then Aaron should get 2 parts out of these 5 equal part

i.e. Aaron gets = 2/5 of the total number of apples = 2/5 of 20 = 2/5 × 20 = 8 apples

Similarly, Ben gets 3 parts out of 5 equal parts

i.e. Ben gets = 3/5 of the total number of apples = 3/5 of 20 = 3/5 × 20 = 12 apples

Therefore, Aaron gets 8 apples and Ben gets 12 apples.

In other way we can solve this by the direct method,

Since, the given ratio = 2 : 3 and 2 + 3 = 5

Therefore, Aaron gets = 2/5 of the total number of apples

= 2/5 × 20 apples = 8 apples

and, Ben gets = 3/5 of the total number of apples

= 3/5 × 20 apples = 12 apples

2. Divide $120 between David and Jack in the ratio 3 : 5. Solution: Ratio of David’s share to Jack’s share = 3 : 5 Sum of the ratio terms = 3 + 5 = 8 Thus we can say David gets 3 parts and Jack gets 5 parts out of every 8 parts. Therefore, David’s share =$(3 × 120)/8 = $45 And, Jack’s share =$(5 × 120)/8 = $75 Therefore, David get$45 and Jack gets $75 More solved problems on dividing a quantity in a given ratio: 3. Divide$260 among A, B and C in the ratio 1/2 : 1/3 : 1/4.

Solution:

First of all convert the given ratio into its simple form.

Since, L.C.M. of denominators 2, 3 and 4 is 12.

Therefore, 1/2 : 1/3 : 1/4 = 1/2 × 12 : 1/3 × 12 : 1/4 × 12 = 6 : 4 : 3

And, 6 + 4 + 3 = 13

Therefore, A’ share = 6/13 of $260 =$6/13 × 260 = $120 B’ share = 4/13 of$260 = $4/13 × 260 =$80

C’ share = 3/13 of $260 =$3/13 × 260 = $60 Therefore, A get$120, B gets $80 and C gets$60

4. Two numbers are in the ratio 10 : 13. If the difference between the numbers is 48, find the numbers.

Solution:

Let the two numbers be 10 and 13

Therefore, the difference between these numbers = 13 – 10 = 3

Now applying unitary method we get,

When difference between the numbers = 3; 1st number = 10

⇒ when difference between the numbers = 1; 1st number = 10/3

⇒ when difference between the numbers = 48; 1st number = 10/3 × 48 = 160

Similarly, in the same way we get;

When difference between the numbers = 3; 1st number = 13

⇒ when difference between the numbers = 1; 1st number = 13/3

⇒ when difference between the numbers = 48; 1st number = 13/3 × 48 = 208

Therefore, the required numbers are 160 and 208.

The above examples on dividing a quantity in a given ratio will give us the idea to solve different types of problems on ratios.