Question

Check whether the following terms are in proportion ? 

1) 5,6,7,8 

2) 3,5,6,10 

3) 4,8,7,14 

4) 2,12,3,18

Answer 1

1) Given, 5, 6, 7, 8 

If a, b, c, d are in proportion i.e., a : b :: c : d 

If 5, 6, 7, 8 are in proportion i.e., 5 : 6 :: 7 : 8 

We know that, product of extremes = Product of means [a x d : b x c] 

5 x 8 = 6 x 7

40 ≠ 42 

So, 5, 6, 7, 8 are not in proportion.

2) Given, 3, 5, 6, 10 

If a, b, c, d are in proportion i.e., a : b :: c : d 

If 3, 5, 6, 10 are in proportion i.e., 3 : 5 :: 6 : 10 

We know that, product of extremes = Product of means a x d = b x c 

3 x 10 = 5 x 6 

30 = 30 

So, 3, 5, 6, 10 are in proportion.

3) Given, 4, 8, 7, 14. 

If a, b, c, d are in proportion i.e., a : b : : c : d 

If 4, 8, 7, 14 are in proportion i.e., 4 : 8 : : 7 : 14 

We know that, product of extremes = Product of means a x d = b x c 

4 x 14 = 8 x 7 = 56 

So, 4, 8, 7, 14 are in proportion.

4) Given, 2, 12, 3, 18 

If a, b, c, d are in proportion i.e., a : b :: c : d 

If 2, 12, 3, 18 are in proportion i.e., 2 : 12 : : 3 : 18 

We know that, product of extremes = Product of means [ a x d = b x c ] 

2 x 18 = 12 x 3 

36 = 36 

So, 2, 12, 3, 18 are in proportion.