JIPMAT 2024 (QA) - The HCF and LCM of two numbers x and y are respectively 6 and 210 . x+y=72, then 1/x+1/y is equal to : | PYQs + Solutions

JIPMAT 2024

Number System

HCF & LCM

Medium

The HCF and LCM of two numbers $\mathrm{x}$ and $\mathrm{y}$ are respectively 6 and 210 .
If $x+y=72$ , then $\frac{1}{x}+\frac{1}{y}$ is equal to :

\frac{1}{35}

\frac{3}{35}

\frac{5}{37}

\frac{2}{35}

Correct Option: 4

1) Given:

\newline

- HCF(

x,y

) =

6

\newline

- LCM(

x,y

) =

210

\newline

x + y = 72

2) We know that for any two numbers:

\newline

x × y = \text{HCF} × \text{LCM}

\newline

- Therefore,

x × y = 6 × 210 = 1260

3) Now we have two equations:

\newline

x + y = 72

\newline

x × y = 1260

4) To find

\frac{1}{x} + \frac{1}{y}

\frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy}

- =

\frac{72}{1260}

- =

\frac{72}{1260}

- =

\frac{36}{630}

- =

\frac{2}{35}

Therefore,

\frac{1}{x} + \frac{1}{y} = \frac{2}{35}