Question
Solve the following simultaneous equations.
$\frac{7 x-2 y}{x y}=5 ; \frac{8 x+7 y}{x y}=15$
$\frac{7 x-2 y}{x y}=5 ; \frac{8 x+7 y}{x y}=15$
✓
Answer
$\frac{7 x-2 y}{x y}=5 \Rightarrow \frac{7 x}{x y}-\frac{2 y}{x y}=5 \Rightarrow \frac{7}{y}-\frac{2}{x}=5 \ldots \text { (I) } $
$\frac{8 x+7 y}{x y}=15 \Rightarrow \frac{8 x}{x y}+\frac{7 y}{x y}=15 \Rightarrow \frac{8}{y}+\frac{7}{x}=15 \ldots (II)$
$\frac{1}{x}=m \text { and } \frac{1}{y}=n $
$7 n-2 m=5 \ldots \text { (III) }$
$8 n+7 m=15 \ldots(\text { IV) }$
Multiply Eq. 1 by 7 and Eq.Il by 2
$49 n -14 m=35 \ldots( V ) 16 n +14 m=30 \ldots( VI ) $
$65 n =65 $
$n =\frac{65}{65} $
$n =1$
Substituting value in Eq.VI
$16 \times 1+14 m=30$
$14 m=30-16 $
$14 m=14$
$m=\frac{14}{14}$
$m=1$
$\therefore \frac{1}{x}= m \Rightarrow \frac{1}{x}=1 \Rightarrow x =1 $
$\frac{1}{ y }= n \Rightarrow \frac{1}{y}=1 \Rightarrow y =1$
Hence, $(x, y)=(1,1)$
$\frac{8 x+7 y}{x y}=15 \Rightarrow \frac{8 x}{x y}+\frac{7 y}{x y}=15 \Rightarrow \frac{8}{y}+\frac{7}{x}=15 \ldots (II)$
$\frac{1}{x}=m \text { and } \frac{1}{y}=n $
$7 n-2 m=5 \ldots \text { (III) }$
$8 n+7 m=15 \ldots(\text { IV) }$
Multiply Eq. 1 by 7 and Eq.Il by 2
$49 n -14 m=35 \ldots( V ) 16 n +14 m=30 \ldots( VI ) $
$65 n =65 $
$n =\frac{65}{65} $
$n =1$
Substituting value in Eq.VI
$16 \times 1+14 m=30$
$14 m=30-16 $
$14 m=14$
$m=\frac{14}{14}$
$m=1$
$\therefore \frac{1}{x}= m \Rightarrow \frac{1}{x}=1 \Rightarrow x =1 $
$\frac{1}{ y }= n \Rightarrow \frac{1}{y}=1 \Rightarrow y =1$
Hence, $(x, y)=(1,1)$
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F.V. = ₹ 100
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→Activity :
F.V. = ₹ 100
Number of shares = 300
Market value = ₹ 120
(a) Sum invested = M.V. × No. of shares
$\therefore$ = ⬜ x ⬜
= ₹ 36,000
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