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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables1 Mark
MCQ
Form the pair of linear equations in the problem, and find its solution graphically $......$
$5$ pencils and $7$ pens together cost $Rs.50$ whereas $7$ pencils and $5$ pens together cost $Rs.46$. The cost of $1$ pen is :
  • A
    $Rs.6$
  • B
    $Rs.3$
  • C
    $Rs.4$
  • ✓
    $Rs.5$
✓

Answer

Correct option: D.
$Rs.5$
Let, cost $($in $RS)$ of one pencil $= x$
and cost $($in $RS$) of one pen $= y$
Therefore, according to question
$5x + 7y = 50 ...(1)$
$7x + 5y = 46 ...(2)$
Multiply equation $(1)$ by $7$ and equation $(2)$ by $5$ we get
$7(5x + 7y) = 7 × 50$
$35x + 49y = 350 ...(3)$ and
$5(7x + 5y) = 5 × 46$
$35x + 25y = 230 ...(4)$
Subtract equation $(4)$ from equation $3,$ we get
$35x + 49y - 35x - 25y = 350 - 230$
$49y - 25y = 120$
$24y = 120$
$\text{y} = \frac{120}{24}$
$y = 5$
Substitute $y = 5$ in equation $1,$ we get
$5x + 7 × 5 = 50$
$5x + 35 = 50$
$5x = 50 - 35$
$5x = 15$
$\text{x} = \frac{15}{15}$
$x = 3$
Cost of One Pen $= y = 5$

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