In this page ratio and proportion solution3 we are going to see solution of each question from the worksheet ratio and proportion.

**How to arrange the given ratios in descending order:**

(i) First write the given ratios in the form of fraction. For example write the ratios a : b as a/b and c : d as c/d

(ii) Now we have to consider the denominators.

(iii) If the denominator are same we can just compare the numerators and write the fractions from greater to smaller.

(iv) If the denominators are not then we have to make them as same by taking L.C.M

(v) Arrange fractions from greater to smaller

(vi) Now we have to write the fractions as ratios.

(3) Arrange the ratios in the descending order

(i) 3 : 4, 5 : 8 and 13 : 16

**Solution:**

3 : 4 = 3/4

5 : 8 = 5/8

13 : 16 = 13/16

Since the denominators are not same,we have to take L.C.M to make them as same.

L.C.M of 4 , 8 ,16 is 16

(3/4) **x** (4/4) = 12/16

(5/8) **x** (2/2) = 10/16

(13/16) **x** (1/1) = 13/16

(13/16) > (12/16) > (10/16)

13 : 16 > 3 : 4 > 5 : 8

Therefore descending order is **13 : 16 > 3 : 4 > 5 : 8**

(ii) 7 : 12 , 13 : 20 , 5 : 8 and 13 : 15

**Solution:**

7 : 12 = 7/12

13 : 20 = 13/20

5 : 8 = 5/8

13 : 15 = 13/15

Since the denominators are not same,we have to take L.C.M to make them as same.

L.C.M of 12 , 20 , 8 and 15 is 120

(7/12) **x** (10/10) = 70/120

(13/20) **x** (6/6) = 78/120

(5/8) **x** (15/15) = 75/120

(13/15) **x** (8/8) = 104/120

(104/120) > (78/120) > (75/120) > (70/120)

(13/15) > (13/20) > (5/8) > (7/12)

13 : 15 > 13 : 20 > 5 : 8 > 7 : 12

Therefore descending order is **13 : 15 > 13 : 20 > 5 : 8 > 7 : 12 **

(iii) 11 : 14 , 17 : 21 , 6 : 7 and 4 : 3

**Solution:**

11 : 14 = 11/14

17 : 21 = 17/21

6 : 7 = 6/7

4 : 3 = 4/3

Since the denominators are not same,we have to take L.C.M to make them as same.

L.C.M of 14 , 21 , 7 and 3 is 42

(11/14) **x** (3/3) = 33/42

(17/21) **x** (2/2) = 34/42

(6/7) **x** (6/6) = 36/42

(4/3) **x** (14/14) = 56/42

(56/42) > (36/42) > (34/42) > (33/42)

(4/3) > (6/7) > (17/21) > (11/14)

4 : 3 > 6 : 7 > 17 : 21 > 11 : 14

Therefore descending order is **4 : 3 > 6 : 7 > 17 : 21 > 11 : 14 **

ratio and proportion solution3 ratio and proportion solution3

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