If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are…
202420252024
If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Answer: C. 11/120 — Let the numbers be a and b. Given a + b = 55, H.C.F. = 5 and L.C.M. = 120. Product of the numbers ab = H.C.F. × L.C.M. = 5 × 120 = 600. Sum of reciprocals =…
- A.
55/601
- B.
601/55
- C.
11/120
- D.
120/11
Attempted by 1461 students.
Show answer & explanation
Correct answer: C
Let the numbers be a and b.
Given a + b = 55, H.C.F. = 5 and L.C.M. = 120.
Product of the numbers ab = H.C.F. × L.C.M. = 5 × 120 = 600.
Sum of reciprocals = 1/a + 1/b = (a + b)/ab = 55/600 = 11/120.
Key fact used: product of two numbers = H.C.F. × L.C.M.
Algebraic simplification: 1/a + 1/b = (a + b)/ab.
Loading lesson…