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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