**Ques - a : b = 4 : 9. If 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b? **

**(a) 80**

**(b) 100**

**(c) 125**

**(d) 130**

**Solution - **

a : b = 4 : 9

Let,

a = 4x

b = 9x

If 4 is added to both of the numbers then the new ratio becomes 21 : 46.

(4x + 4)/(9x + 4) = 21/46

46 (4x + 4) = 21(9x + 4)

184x + 184 = 189x + 84

184 - 84 = 189x - 184x

100 = 5x

**x = 20**

Therefore,

a = 4x

a = 4(20)

**a = 80**

b = 9x

b = 9(20)

**b = 180**

So,

b - a = 180 - 80

**= 100**

Thus,

**The difference between a and b is 100.**

Hence,

The correct answer is option **(b) 100.**

Thank You