Question:medium

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

Show Hint

Even when asked for a graphical solution, always solve the system algebraically on your rough sheet first!
This gives you the exact intersection point \((1, 3)\), ensuring your hand-drawn lines on the graph are perfectly aligned and pass through the correct grid intersections.
Updated On: Jul 7, 2026
  • Pencil = Rs 1, Chocolate = Rs 3
  • Pencil = Rs 2, Chocolate = Rs 3
  • Pencil = Rs 1, Chocolate = Rs 4
  • Pencil = Rs 3, Chocolate = Rs 1
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Set up the same two equations, then solve by elimination instead of by plotting points.
Let the price of one pencil be Rs $x$ and the price of one chocolate be Rs $y$. From the given information:
\[ 2x + 3y = 11 \quad \text{...(1)} \]
\[ x + 2y = 7 \quad \text{...(2)} \]

Step 2: Make the $x$-coefficients match so one variable can be cancelled by subtraction.
Multiply equation (2) by 2, so its $x$-coefficient becomes 2, matching equation (1):
\[ 2x + 4y = 14 \quad \text{...(3)} \]

Step 3: Subtract equation (1) from equation (3) to eliminate $x$.
\[ (2x + 4y) - (2x + 3y) = 14 - 11 \]
\[ y = 3 \]

Step 4: Substitute this value of $y$ back into equation (2) to find $x$.
\[ x + 2(3) = 7 \]
\[ x + 6 = 7 \]
\[ x = 1 \]

Step 5: Interpret the result, and check that the two lines from these equations do meet exactly at this point, matching the graphical picture.
Since $(x, y) = (1, 3)$ satisfies both original equations at once, this is exactly the point where the two lines representing them would cross if plotted, confirming the same intersection point the graphical method is meant to find.

Step 6: Final Answer.
The price of one pencil is Rs 1 and the price of one chocolate is Rs 3, so option (A) is correct. \[ \boxed{\text{Pencil} = \text{Rs } 1,\ \text{Chocolate} = \text{Rs } 3} \]
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