RATIO AND PROPORTION CLASS -9 NOTES BY GO WITH NOTES

 

1. Summary:
2. a, b, c, d are in proportion if a/d = b/c
3. Mean proportional:
4. If a: b:: b: c, then a/b = b/c
5. b2 = ac
   b = √ac
6. Duplicate Ratio: The duplicate ratio of (a : b) is (a2 : b2)
7. Sub-Duplicate Ratio: The sub-duplicate ratio of (a: b) is 
   
8. Triplicate Ratio: The Triplicate ratio of (a : b) is (a3 : b3)
9. Sub-Triplicate Ratio: The sub-triplicate ratio of (a: b) is (a1/3: b1/3)
   

1. If a: b = 5 : 9 and b : c = 4 : 7, find a : b : c.
2. Find the fourth proportional of 5, 8, 15.
3. If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4 , then find the first part.
4. A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4, amounting to Rs. 206. Find the number of coins of each type.
5. The third proportional of 0.36 and 0.48 is
6. If 2A = 3B and 4B = 5C, then A : C is
7. If x : y = 5 : 2, then (8x + 9y) = (8x + 2y) is
8. Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
9. The ratio of three numbers is 3 : 4 : 7 and their product is 18144. The numbers are:
10. What least common number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders may be proportional?