# Ratio

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?

let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x – 3x = 1000

B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000

Example 1:
In a bag of red and green mint sweets, the ratio of red mint sweets to green sweets is 3:4. If the bag contains 120 green mint sweets, how many red mint sweets are there?

Solution:
Let x = number of red sweets.

Write the items in the ratio as a fraction.

3 × 120 = 4 × x
360 = 4x

Answer: There are 90 red sweets.

Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Let x = number of red shirts
and y = number of green shirts

Write the items in the ratios as fractions.

3 × 20 = x × 4
60 = 4x
x = 15

5 × 20 = y × 4
100 = 4y
y = 25

The total number of shirts would be 15 + 25 + 20 = 60