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The sum of 2 numbers is 33 and their HCF and LCM are 3 and 90 respectively. What is the difference of the reciprocals of two numbers?
1. 1/60
2. 1/30
3. 1/90
4. - 1/30

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Best answer
Correct Answer - Option 3 : 1/90

Given: 

HCF = 3

LCM = 90

Calculation:

Let assume the number be 3a

and the second number be 3b

According to question:

3a + 3b = 33

⇒ a + b = 11      ----(1)

LCM od 3a and 3b = 3ab

So, 3ab = 90

⇒ ab = 30      ----(2)          

From equation (1) and equation (2)

a = 5

b = 6

⇒ The first number is = 3a = 3 × 5 = 15

⇒ The second number is = 3b = 3 × 6 = 18

The difference of reciprocal of numbers

⇒ 1/15 - 1/18 = 1/90 

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