Question

HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numb
80. Find the sum of the reciprocals of these numbers.
A) 15/242 B) 16/275 C) 32/221 D) 20/268 E) None of these
Duh​

Answer 1

Let the two numbers be x and y respectively,

According to the question,

✪ HCF(x, y) = 5

✪ LCM(x, y) = 275

Also,

✪ x + y = 80 ...(1)

We know,

==> product of numbers = HCF × LCM

==> x × y = 1375 ...(2)

To Find: 1/x + 1/y

$</p><p> \sf \rightarrow \quad \dfrac{1}{x} + \dfrac{1}{y} \\ \\</p><p> \sf \rightarrow \quad \dfrac{x + y}{xy} \\ \\ \sf \quad from \: (1) \: and \: (2) \\ \\</p><p> \sf \rightarrow \quad \dfrac{80}{1375} \\ \\ \sf \rightarrow \quad \dfrac{16}{275} \\ \\ \sf Hence, \: Option \: ( B ) \: is \: correct.</p><p>$

Answer 2

Answer:

Let the two numbers be x and y respectively,

According to the question,

✪ HCF(x, y) = 5

✪ LCM(x, y) = 275

Also,

✪ x + y = 80 ...(1)

We know,

==> product of numbers = HCF × LCM

==> x × y = 1375 ...(2)

To Find: 1/x + 1/y

\begin{lgathered}\sf \rightarrow \quad \dfrac{1}{x} + \dfrac{1}{y} \\ \\ \sf \rightarrow \quad \dfrac{x + y}{xy} \\ \\ \sf \quad from \: (1) \: and \: (2) \\ \\ \sf \rightarrow \quad \dfrac{80}{1375} \\ \\ \sf \rightarrow \quad \dfrac{16}{275} \\ \\ \sf Hence, \: Option \: ( B ) \: is \: correct.\end{lgathered}

→

x

1

+

y

1

→

xy

x+y

from(1)and(2)

→

1375

80

→

275

16

Hence,Option(B)iscorrect.

bags hope it helps