 |
| Illustrative Examples |
|
| Example 1: |
| |
| Find the compounded ratio of |
| |
| a) 5:14 and 7:15 |
| |
| b) a+b:a-b; (a2-b2):(a2+b2) and a2+b2:(a+b)2 |
| |
| Suggested answer: |
| |
| a) The compounded ratio of 5:14 and 7:15 is |
| |
 |
| |
| b)The compounded ratio of a+b:a-b; a2-b2:a2+b2 and a2+b2:(a+b)2 is (a+b) (a2-b2) (a2+b2) : (a-b) (a2+b2) (a+b)2 |
| |
| (a+b) (a+b) (a-b) : (a-b) (a+b) (a+b) |
| |
| |
| |
| 1:1 |
| |
| Example 2: |
| |
| If x:y=3:4 find value of (4x+3y) : (2x+5y). |
| |
| Suggested answer: |
| |
 |
| |
  |
| |
 |
| |
| Example 3: |
| |
| If 2x - y : 3x - 2y = 3:4, find x:y. |
| |
| Suggested answer: |
| |
  |
| |
| 4(2x-y)=3(3x-2y) |
| |
| 8x-4y=9x-6y |
| |
| |
| |
| 6y-4y=9x-8x |
| |
| 2y=x |
| |
 |
| |
| x:y=2:1 |
| |
| Example 4: |
| |
| In the ratio 7:8, if the consequent is 40, what is the antecedent? |
| |
| Suggested answer: |
| |
  |
| |
 |
| |
| x=35 |
| |
| Antecedent=35. |
| |
| Example 5: |
| |
| If a:b = 5:8. Find the value of a2b+ab2:a3+b3. |
| |
| Suggested answer: |
| |
 |
| |
 |
| |
 |
| |
| |
| |
 |
| |
 |
| |
| |
| |
 |
| |
| Example 6: |
| |
| Find |
| |
| a) reciprocal ratio of 3:5 |
| |
| b) duplicate ratio of 2:3 |
| |
| c) triplicate ratio of 3:4 |
| |
| d) sub duplicate ratio of 25:16 |
| |
| e) sub triplicate ratio of 27:8 |
| |
| Suggested answer: |
| |
| a) Reciprocal ratio of 3:5 |
| |
 |
| |
| b) Duplicate ratio of 2:3 |
| |
| =22:32=4:9 |
| |
| c) Triplicate ratio of 3:4 |
| |
| = 33:43 |
| |
| = 27:64 |
| |
| d) Sub duplicate ratio of 25:16 |
| |
 |
| |
| =5:4 |
| |
| e) Sub triplicate ratio of 27:8 |
| |
 |
| |
| = 3:2 |
| |
| Example 7: |
| |
| If a:b=4:5, b:c=6:7, find a:c and a:b:c. |
| |
| Suggested answer: |
| |
 |
| |
| |
| |
 |
| |
 |
| |
| Hence a:c = 24:35 |
| |
| {a:b = 4:5} x 6 |
| |
| {b:c = 6:7} x 5 |
| |
| a:b = 24:30 |
| |
| b:c = 30:35 (To make b equal in both ratio) |
| |
| Hence a:b:c = 24:30:35 |
| |
| Example 8: |
| |
 |
| |
| Suggested answer: |
| |
 |
| |
 |
| |
| 12a+18 = 25a-190 |
| |
| 25a-12a = 18+190 |
| |
| 13a = 208 |
| |
 |
| |
| a = 16 |
| |
| Example 9: |
| |
| Two numbers are in the ratio 3:4. If 8 is added to the numbers, the ratio becomes 5:6. Find the numbers. |
| |
| Suggested answer: |
| |
 |
| |
 |
| |
| 6x+48 = 5y+40 |
| |
 |
| |
 |
| |
 |
| |
| y = 16 |
| |
 |
| |
 |
| |
| Example 10: |
| |
| Divide Rs.256 in the ratio 7:9. |
| |
| Suggested answer: |
| |
| Let x be common to the ratio 7:9. |
| |
| 7x, 9x |
| |
| 7x+9x=256 |
| |
| 16x=256 |
| |
 |
| |
| Hence, the parts are 7 x 16 = Rs.112 |
| |
| and 9 x 16 = Rs.144. |
| |
