## RATIO AND PROPORTION - ESSENTIAL POINTS

• Ratio: A ratio compares two quantities using a particular operation.
• For example, while comparing heights of two persons with heights 150 cm and 75 cm, we write it as the ratio 150 : 75 or 2 : 1.
• Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent.
• If two ratios are equivalent then the four quantities are said to be in proportion. For example, the ratios 8 : 2 and 16 : 4 are equivalent therefore 8, 2, 16 and 4 are in proportion.
• If a : b : : c : d, then a X d = b X c.
• To calculate the ratio, the numbers have to be of the same unit.

Examples

Example 1 : Divide Rs 2,133 into three parts such that 3 times the first part, 4 times the second part and 2 times the third part are equal

Solution :

Let the part be y

Hence 3y + 4y + 2y = 2,133

9y = 2,133.

Hence y = 2,133/9

y = 237

So 237 X 3, 237 X 4 + 237 X 2 =  Rs 711, Rs 948, Rs 474.

Example 2 : The ratio of students present to students absent is 10 : 2. If the students absent are 6, then find the students present

Solution

10:2 :: x : 6

10 X 6 = 2 X x

2x = 60

x = 30