ICSE Class X Math 2015 Solved Paper

Question : 50 of 52

Marks: +1, -0

Sum of two natural numbers is 8 and the difference of their reciprocal is

\;{2}/{15}

. Find the numbers.

Solution:

Let 1 st no. be

x

and 2 nd be

8-x

.
By the given condition,

\;\;{1}/{x}-\;{1}/{8-x}=\;{2}/{15}

\;⇒ \;\; \;{8-x-x}/{x(8-x)}=\;{2}/{15}

\;⇒ \;\; \;{8-2 x}/{8 x-x^2}=\;{2}/{15}

⇒ \;\; 120-30 x\;=16 x-2 x^2

2 x^2-46 x+120\;=0

x^2-23 x+60\;=0

x^2-20 x-3 x+60\;=0

x(x-20)-3(x-20)\;=0

(x-3)(x-20)\;=0

x=3 \;\text " or "\; x\;=20 \;\text " (not possible) "\;

1^{\;\text "st "\;} \;\text " no. "\;=3

\;\text " and "\; 2^{\;\text "nd "\;} \;\text " no. "\;\;=8-3=5 .

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