Maths - Ratio and Proportion

• Compounded Ratio of two ratios a/b and c/d is ac/bd, i.e., ac : bd.
  Duplicate ratio of a : b is a² : b²,         Triplicate ratio of a : b is a³ : b³
  Reciprocal ratio of a : b is b : a
• Proportion. If four numbers a, b, c, d are in proportion, written as a : b :: c : d, ie a/b = c/d
• Invertendo. If a : b :: c : d then b : a :: d : c,   Alternendo. If a : b :: c : d then a : c :: b : d
  Componendo. If a : b :: c : d then (a +b) : b :: (c +d) : d
  Dividendo. If a : b :: c : d then (a -b) : b :: (c -d) : d
  Componendo and dividendo: If a : b :: c : d then (a +b) : (a -b) :: (c +d) : (c -d)
      i.e., a/b = c/d => (a +b)/(a - b) = (c +d)/(c +d)
• If a/b = c/d = e/f = ..., then each ratio = (a +c +e +...)/(b +d +f +...)

1. If A : B = 8 : 15, B : C = 5 : 8 and C : D = 4 : 5 than A : D is .

          a. 2 : 7 b. 4 : 15 C. 8 : 15 d. 15 : 4 e. None

2. If 2A = 3B and 4B = 5C than A : C is:

          a. 4 : 3 b. 8 : 15 c. 15 : 8 d. 3 : 4 e. None

  3. Two numbers are in the ratio of 1 : 2. If 7 is added to both the ratio is to 3 : 5. The greatest no:

          a. 24 b. 26 c. 28 d. 32 e. None

4. In a bag, there are coins of 25 paisa, 10 paisa & 5 paisa in 1 : 2 : 3 ratio. Their sum is Rs. 30 how many 5 paisa coins are there?

          a. 50 b. 100 c. 150 d. 200 e. None

5. Salaries of Ravi & Sumit are in 2 : 3 ratio. If salary of each is increased by Rs 4000, new ratio becoms 40 : 57. Sumits present salary?

          a. 17000 b. 20000 c. 25500 d. 30000 e. None

6. Two no are respectively 20% & 50% more than a third numbers. The ratio of two no are:

          a. 2 : 5 b. 3 : 5 c. 4 : 5 d. 6 : 7 e. None

7. In a mixture of 60 litres, water and milk is in 2 : 1 ratio. If this ratio is to be 1 : 2, than the quantity of water to be added is:

         a. 20 litres b. 30 litres c. 40 litres d. 60 litres e. None

8. The fourth proportional to 5, 8, 15 is:

         a. 18 b. 24 c. 19 d. 20 e. 21 

9. The ages of A & B are in 3 : 1. Fifteen years hence the ratio will be 2 : 1. Their present age is:

a. 30 & 10 b. 45 & 15 c. 21 & 7 d 60 & 20 e. None

10. If 10% of x = 20% of y, then x : y is:

       a. 1 : 2 b. 2 : 1 c. 5 : 1 d. 10 : 1 e. None

11. The compount ratio of (2 : 3), (6 : 11) & (11 : 2) is:

        a. 1 : 2 b. 2 : 1 c. 11 : 24 d. 36 : 121 e. None
Ans: 1b, 2c, 3c, 4c, 5d, 6c, 7d, 8b, 9b, 10b, 11b.