Select the option that is true regarding the following labelled Assertion (A) and Reason (R).

Assertion (A)	Reason (R)
The cost of 5 pens, 6 erasers and 7 notebooks is ₹340 and the cost of 6 pens, 4 erasers and 2 notebooks is ₹200. The cost of one pen, one eraser and 1 notebook is ₹55.	Let x, y and z denote the cost of 1 pen, 1 eraser and 1 notebook, respectively. 5x + 6y + 7z = 340 and 6x + 4y + 2z = 200.

Correct option is A

Given:

Solution:

Assertion (A):

• The cost of 5 pens, 6 erasers, and 7 notebooks is ₹340
• The cost of 6 pens, 4 erasers, and 2 notebooks is ₹200
• The cost of 1 pen + 1 eraser + 1 notebook = ₹55

Let:

• x = cost of 1 pen
• y = cost of 1 eraser
• z = cost of 1 notebook

From the data, we get these equations:

1. 5x + 6y + 7z = 340
2. 6x + 4y + 2z = 200
3. x + y + z = 55

Check if equation 3 fits equations 1 and 2:

Multiply equation (3) by 2:
→ 2x + 2y + 2z = 110

Now subtract from equation (2):
(6x + 4y + 2z) − (2x + 2y + 2z) = 200 − 110
→ 4x + 2y = 90 → equation (4)

Now multiply equation (3) by 5:
→ 5x + 5y + 5z = 275

Now subtract from equation (1):
(5x + 6y + 7z) − (5x + 5y + 5z) = 340 − 275
→ y + 2z = 65 → equation (5)

Solve equations (4) and (5):

From equation (4):
→ 2x + y = 45 → y = 45 − 2x

Substitute y into equation (5):
(45 − 2x) + 2z = 65
→ 2z = 20 + 2x → z = 10 + x

Now substitute y and z into equation (3):
x + (45 − 2x) + (10 + x) = 55
→ x − 2x + x + 45 + 10 = 55
→ 55 = 55 Verified

Conclusion:

• Assertion is true — the total of pen + eraser + notebook = ₹55
• Reason is true — equations given are correct
• Reason correctly explains the Assertion

Final Answer: (A) Both A and R are true and R is a correct explanation of A