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.
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