Download App

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

Gujarat BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two Variables3 Marks
Question
Form the pair of linear equations in the problem, and find its solution graphically:
$5$ pencils and $7$ pens together cost $₹\ 50$ whereas $7$ pencils and $5$ pens together cost $₹\ 46.$ Find the cost of one pencil and that of one pen.
✓

Answer

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
$7(5x+7y)= 7 \times 50$
$35x +49y = 350 .......(3)$
and
$5(7x +5y) = 5 \times 46$
$35x +25y = 230 ....... (4)$
Subtract equation $(4)$ from equation $3 ,$ we get
$35x + 49y - 35x - 25y = 350 -230$
$49y -25y = 120$
$24y = 120$
$y = \frac{120}{24}$
$y= 5$
Substitute $y = 5$ in equation $1 ,$ we get
$5x + 7 \times 5 =50$
$5x + 35 = 50$
$5x = 50 - 35$
$5x = 15$
$x= \frac{15}{5}$
$x=3$
Hence, Cost of One Pen $= y =5$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Pair of Linear Equations in Two Variables→Pair of Linear Equations in Two Variables — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is $9\ cm$.
→
Write the zeros of the polynomial $x^2- x - 6.$
→

Evaluate the following:

$(\cos0^\circ+\sin45^\circ+\sin30^\circ)(\sin90^\circ-\cos45^\circ+\cos60^\circ)$

→
Find the coordinates of the midpoint the line segment joining:
  1. $A(3, 0)$ and $B(-5, 4)$
  2. $P(-11, -8)$ and $Q(8, -2).$
→
Name the type of quadrilateral formed, if any, by the points $(4,5),(7,6),(4,3),(1,2)$, and give a reason for your answer.
→
Evaluate the following:
$\frac{\sin30^\circ}{\sin45^\circ}+\frac{\tan45^\circ}{\sec60^\circ}-\frac{\sin60^\circ}{\cot45^\circ}-\frac{\cos30^\circ}{\sin90^\circ}$
→
Find a quadratic polynomial whose zeros are $2$ and $-5.$
→
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\sin\text{A} = \frac{2}{3}$
→
Express the $HCF$ of $468$ and $222$ as $468x + 222y$ where $x, y$ are integers in two different ways.
→
If the area of a circle is numerically equal to twice its circumference then what is the diameter of the circle?
→