Rules of dividing a quantity in two given ratios is explained below along with the different types of examples.
If a quantity K is divided into two parts in the ratio X : Y, then
First part = X/(X + Y) × K,
Second part = Y/(X + Y) × K,
Solved examples:
1. Two numbers are in the ratio 7 : 6. If the sum of the numbers is 91, find the numbers.
Solution:
Sum of the terms of the ratio = 7 + 6 = 13.
First number = 7/13 × 91 = 49.
Second number = 6/13 × 91 = 42.
Thus, the numbers are 49 and 42.
2. 12 sweets are to be divided between A and B in the ratio 1 : 3. Find how many sweets does each gets?
Solution:
Here, A and B gets sweets in the ratio 1 : 3.
This means, if the sweets are divided in 1 + 3 = 4 equal parts.
Then, A gets = 1/4 of the total number of sweets.
= 1/4 × 12 sweets = 3 sweets.
And, B gets = 3/4 of the total number of sweets.
= 3/4 × 12 sweets = 9 sweets.
3. The pole of length 165 cm is divided into two parts such that their lengths are in the ratio 7 : 8. Find the length of each part of the pole.
Solution:
Here, 165 cm is to be divided into two lengths in the ratio 7 : 8 and 7 + 8 = 15.
Therefore, length of one (shorter) part = 7/15 × 165 cm = 77 cm.
And, length of other (longer) part = 8/15 × 165 cm = 88 cm.
4. The total weight of the mixture of two things A and B is 50 kg. If A and B are mixed in the ratio 3 : 7; find the quantity of B in the mixture.
Solution:
Since, A and B are mixed in the ratio 3 : 7 and, 3 + 7 = 10.
Therefore, quantity of B in the mixture = 7/10 × 50 kg
= 35 kg
The above examples on dividing a quantity in two given ratios will help us to solve different types of problems on ratios.
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