Dividing a Quantity in Two given Ratios

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.






6th Grade Page

From Dividing a Quantity in Two given Ratios to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.