In this page ratio and proportion solution8 we are going to see solution of each question from the worksheet ratio and proportion.

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

(8) Find the duplicate ratio of

(i) 9 : 16

**Solution:**

= √9 : √16

= √(3 **x** 3) : √(4 **x** 4)

= 3 : 4

Therefore the duplicate ratio of 9 : 16 is **3 : 4**

(ii) (1/25) : (1/36)

**Solution:**

= √(1/25) : √(1/36)

= √1/(5 **x** 5) : √1/(6 **x** 6)

= (1/5) : (1/6)

= (1/5)/(1/6)

= (1/5)**x **(6/1)

= (6/5)

= 6 : 5

Therefore the duplicate ratio of (1/25) : (1/36) is **6 : 5**

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

(9) Find the sub-triplicate ratio of

(i) 27 : 125

**Solution:**

= ∛27 : ∛125

= ∛(3 **x** 3** x** 3) :
∛(5 **x** 5** x** 5)

= 3 : 5

Therefore the sub-triplicate ratio of 27 : 125 is **3 : 5**

(ii) (64/x³) : (125/y³)

**Solution:**

= ∛(64/x³) : ∛(125/y³)

= ∛(4 **x** 4** x** 4)/(x³) :
∛(5 **x** 5** x** 5)/(y³)

= (4/x) : (5/y)

= (4/x)/(5/y)

= (4/x) **x** (y/5)

= (4y/5x)

= 4y : 5x

Therefore the sub-triplicate ratio of (64/x³) : (125/y³) is **4y : 5x **

(iii) (1/216) : (1/343)

**Solution:**

= ∛(1/216) : ∛(1/343)

= ∛1/(6 **x** 6** x** 6) :
∛1/(7 **x** 7** x** 7)

= (1/6) : (1/7)

= (1/6)/(1/7)

= (1/6) **x** (7/1)

= (7/6)

= 7 : 6

Therefore the sub-triplicate ratio of (1/216) : (1/343) is **7 : 6 **

The reciprocal ratio of a : b is (1/a) : (1/b) that is b : a

(10) Find the reciprocal ratio of

(i) 3/p : 2/q

**Solution:**

The reciprocal ratio of 3/p : 2/q is 1/(3/p) : (1/(2/q))

= 1/(3/p) : (1/(2/q))

= (p/3) : (q/2)

= (p/3)/(q/2)

= (p/3) x (2/q)

= (2p/3q)

= **2 p : 3 q**

(ii) (1/4) : (1/9)

**Solution:**

The reciprocal ratio of (1/4) : (1/9) is 1/(1/4) : (1/(1/9))

= 1/(1/4) : (1/(1/9))

= (4/1) : (9/1)

= (4/1)/(9/1)

= (4/1) x (1/9)

= (4/9)

= **4 : 9**

ratio and proportion solution8 ratio and proportion solution8

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