Ratios and Proportions Test

1. John has an income of $30000 and he pays $6000 as income tax. Find the ratio of:
   [A] His income tax to income
   [B] Income to income tax
   (click for answer)

   Income of John = $30000
   Income tax = $6000

   [A] Ratio of income tax to income = 6000:30000 = 6000/30000 = 1/5 = 1:5.
   [B] Ratio of income to income tax = 30000:6000 = 30000:6000 = 5/1 = 5:1

2. If Adam ran 2 km on Monday and ran just 500 m on Tuesday, then what is the ratio of distance run by Adam on Tuesday to Monday? (click for answer)

   Distance run by Adam on Tuesday = 500m
   Distance run by Adam on Monday = 2 kilometers = 2000 meters ( as 1km = 1000 meters)
   (Tip: It is always important to convert both the items into a common unit as ratio could only be achieved between quantities of same units)

   Therefore, ratio of distance run by Adam on Tuesday to Monday
   = 500:2000
   = 500/2000
   = 1/4
   = 1:4

3. Jake works in a software company and earns $1000 per month. From that, he saves $200 per month. What is the ratio of Jake’s savings to income? (click for answer)

   Savings of Jake per month = $200
   Income of Jake per month = $1000
   Ratio of Jake’s savings to income per month = 200:1000 = 200/1000 = 2/5 = 2:5

4. The first and the fourth terms of a proportion are 9 and the second term is 27. Find out the third term? (click for answer)

   1st term = 9
   2nd term = 27
   3rd term = ?
   4th term = 9

   Let the third term be ‘m’.

   Therefore,

   27 x m = 9 x 9 ( by cross product multiplication)
   27m = 9 x 9
   27m = 81
   m = 81/27
   m = 3

   Therefore, the 3rd term is 3

5. Is the statement true?
   16:32 = 10:20 (click for answer)

   After putting the ratios in fraction form and by using cross product multiplication, we get 16 x 20 = 320 and 10 x 32 = 320. You may also reduce the fractions, which would be 1/2 = 1/2. Therefore, the products are same and the statement is TRUE.