Question

Sum of two no is 15. If the sum of their reciprocal is 3/10.find the number

Answer 1

Let the numbers be x&y

According to question, x+y = 15 &

$\frac{1}{x} + \frac{1}{y} = \frac{1}{10} \\ \frac{x + y}{xy} = \frac{3}{10} \\ \frac{15}{xy} = \frac{3}{10} \\ xy = \frac{15 \times 10}{3} = 50 \\ x = \frac{50}{y}$

$∴ \frac{50}{y} + y = 15 \\ 50 + {y}^{2} = 15y \\ {y}^{2} - 15y + 50 = 0 \\ {y}^{2} - 10y - 5y + 50 = 0 \\ y(y - 10) - 5(y - 10) = 0 \\ (y - 10)(y - 5) = 0 \\ \\ ∴y = <strong>5</strong><strong>,</strong><strong>1</strong><strong>0</strong>$

Answer 2

$\huge \sf \color{purple}{\underline{\underline{Answer}}} :$

Two numbers are 5 and 10

$\huge \sf \color{purple}{\underline{\underline{Solution}}}:$

✯ Let the number be x .

✯ Then the other number is 15 - x.

$\sf \color{brown}{Using \: the \: given \: information \: , we\: get }$

$\sf \frac{1}{x}+\frac{1}{15-x}=\frac{3}{10} \\ \\ \sf \frac{15-x+x}{x(15-x)}=\frac{3}{10} \\ \\ \sf \frac{15}{(15x-x²)}=\frac{3}{10} \\ \\ \sf 150=45x-3x² \\ \\ \sf 3(x²-15+50)=0 \\\\ \sf x²-15+50=0 \\ \\ \sf x²-5x-10x+50 =0 \\ \\ \sf (x-10)(x-5)=0 \\ \\ \sf x-10=0 \: \: \ \ \ OR \ \ \ \ \sf x-5 \\ \\ \sf \boxed{ \colorbox{lightgreen}{x=10}} \ \ \ \ or \ \ \ \ \boxed{\colorbox{lightgreen}{ x = 5 }}$

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When x = 10 , then the other number is 15-5 = 10

When x = 5, then the other number is 15-5 = 10

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$\sf \color{blue}{Hence, \ the \ two \ numbers \ are \ 5 \ and \ 10 }$

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