Q) 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.

(Q 33 – 30/2/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s consider price of 1 pencil is X and price of 1 chocolate is Y.

Next, by given condition “Aarush bought 2 pencils and 3 chocolates for Rs. 11”

∴ we can write it as 2 X + 3 Y = 11 …………. (i)

Step 2: Next condition is: 2. “Tanish bought 1 pencil and 2 chocolates for Rs. 7”

∴ we can write it as X + 2 Y = 7 ………… (ii)

These 2 linear equations represent the situation

Step 3: Next, Let’s find values of X and Y by solving these 2 eqiations:

By multiplying equation (ii) by 2, we get:

2X + 4 Y = 14 …………… (iii)

Now, we subtract equation (i) from equation (iii), we get:

(2 X + 4 y) – (2 X + 3 Y) = 14 – 11

∴ 2 X + 4 Y – 2 X – 3 Y = 3

∴ Y = 3

Step 4: Now, we substitute value of Y in equation (ii), we get:

X + 2 Y = 7

∴ X + 2 (3) = 7

∴ X + 6 = 7

∴ X = 7 – 6 = 1

Therefore, price of one pencil is Rs. 1 and the price of one chocolate is Rs. 3.

Step 5:  tNext, we plot these two equations:

It is clear that the two linear equation intersect each other at point (1, 3). Hence, this is the solution of these equations.

Here X = 1 => price of one pencil is Rs. 1 and Y = 3 => the price of one chocolate is Rs. 3.

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Final Thoughts on Linear Equations:

We hope this Step-by-Step Solution for the Pencils and Chocolates problem clarifies how to frame and solve Linear Equations in Two Variables. Following the correct method is crucial for scoring full marks in Class 10 Maths Board Exams. This type of word problem is a favorite in NCERT and CBSE Previous Year Papers. For more detailed solutions and practice sets, stay connected with Sapling Academy!