Question

The sum of 2 numbers is 15 and the sum of their reciprocals is 3/10 fnd the number ?

Answer 1

Let one no be x.
Other =15-x
reciprocal=1/x and 1/(15-x)
According to the problem,
1/x+1/15-x=3/10
Or, (15-x+x)/[x(15-x)]=3/10 {LCM}

Or,15*10=45x-3x^2{CROSS
MULTIPLICATION}

Or,150-45x+3x^2=0{MIDDLE TERM BREAKING}

Or,150-15x-30x+3x^2=0

Or 15(10-x)-3x(10-x)=0

Or(,15-3x)(10-x)=0

Either,

15-3x=0
Or,x=5

Or

10-x=0
Or, x=-10

Therefore
In this case x=5
Nos are 5and 10.
(There sum of reciprocal =3/10.)
Ans :nos are 5 and 10

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