Question

The sum of the two numbers is 150 and their HCF is 15. If the numbers are in between 40 and 120, then the sum of their reciprocals is:
1. \(\dfrac{1}{105}\)
2. \(\dfrac{2}{63}\)
3. \(\dfrac{3}{115}\)
4. \(\dfrac{2}{65}\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{2}{63}\)

Calculation:

H.C.F. = 15

Let the number be 15x and 15y

15x + 15y = 150

x + y= 10

Since x and y, should be co - prime because their H.C.F is already given as 15

x + y = 10, if x and you co-prime then

x or y = 7 and. x or y = 3

Take x = 7 and y = 3

Two numbers = 15x = 15 × 7 = 105

⇒ 15y = 15 × 3 = 45

According to the question,

1/15x + 1/15y 

⇒ 1/105 + 1/45

⇒ (3 + 7)/315

⇒ 10/315 = 2/63

∴ The sum of their reciprocals is 2/63.