In this page ratio and proportion solution7 we are going to see solution of each question from the worksheet ratio and proportion.

To find the duplicate ratio of any ratios we have to take square.

(6) Find the duplicate ratio of

(i) √2 : 3

**Solution:**

= (√2)² : (3)²

= 2 : 9

Therefore the duplicate ratio of √2 : 3 is 2 : 9

(ii) 5 : 6

**Solution:**

= (5)² : (6)²

= 25 : 36

Therefore the duplicate ratio of 5 : 6 is 25 : 36

(iii) a : a^(3/2)

**Solution:**

= (a)² : (a^(3/2))²

= (a)² : (a^(3/2) **x** 2)

= a² : a³

Therefore the duplicate ratio of a : a^(3/2) is a² : a³

(iv) (1/3) : (1/4)

**Solution:**

= (1/3)² : (1/4)²

= (1/9) : (1/16)

= (1/9)/(1/16)

= (1/9)/(16/1)

= (16/9)

= 16 : 9

Therefore the duplicate ratio of (1/3) : (1/4) is 16 : 9

To find the triplicate ratio of any ratios we have to take cube.

(7) Find the triplicate ratio of

(i) 2 : 5

**Solution:**

taking cubes for both antecedent and consequent

= (2)³ : (5)³

= 8 : 125

Therefore the duplicate ratio of 2 : 5 is **8 : 125**

(ii) 2^(1/3) : 3^(1/3)

**Solution:**

taking cubes for both antecedent and consequent

= (2^(1/3))³ : (3^(1/3))³

= (2^(1/3) **x** 3) : (3^(1/3)** x** 3)

= 2 : 3

Therefore the duplicate ratio of 2^(1/3) : 3^(1/3) is **2 : 3**

(iii) √a : √b

**Solution:**

taking cubes for both antecedent and consequent

= ( √a)³ : ( √b)³

= (a^(1/2) **x** 3) : (b^(1/2)** x** 3)

= a^(3/2) : b^(3/2)

Therefore the duplicate ratio of √a : √b is **a^(3/2) : b^(3/2) **

(iv) (1/5) : (1/7)

**Solution:**

taking cubes for both antecedent and consequent

= (1/5)³ : (1/7)³

= (1/125) : (1/343)

= (1/125)/(1/343)

= (1/125)x (343/1)

= (343/125)

= 343 : 125

Therefore the duplicate ratio of (1/5) : (1/7) is **343 : 125**

ratio and proportion solution7 ratio and proportion solution7

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- Time and Work
- Time and Distance
- Ratio and Proportion
- Average
- Percentage
- Profit and Loss
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- Odd man out
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