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

Assertion (A)	Reason (R)
The cost of 3 vadas and 4 samosas is ₹195. If the cost of a samosa increases by 10% and that of a vada decreases by one-fifth, the cost of 2 vadas and 3 samosas is ₹139. The original cost of 2 vadas and 1 samosa is ₹80.	Let cost of 1 vada and 1 samosa is ₹ $$x$$​ and ₹ $$y$$​, respectively. $$3x+4y=195$$​ and $$2×(1.1)x+3×\frac{1}{5}y=139$$​.

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Correct option is A

Given:

Solution:

Let:

• Cost of 1 vada = x
• Cost of 1 samosa = y

Step 1: Use the first condition from Assertion (A):

Cost of 3 vadas and 4 samosas = 195

So,
3x + 4y = 195 — (Equation 1)

Step 2: Use the second condition from Assertion (A):

Vada price decreases by one-fifth (20%) → new price = 0.8x
Samosa price increases by 10% → new price = 1.1y
Cost of 2 vadas and 3 samosas after the change = 139

So,
2 × 0.8x + 3 × 1.1y = 139
1.6x + 3.3y = 139 — (Equation 2)

Step 3: Solve the equations

Multiply Equation 2 by 5 to eliminate decimals:

8x + 16.5y = 695 — (Equation 3)

Now multiply Equation 1 by 2.6667 (to get 8x):

8x + 10.667y = 520 — (Equation 4)

Subtract Equation 4 from Equation 3:

(16.5y - 10.667y) = 695 - 520
5.833y = 175
y = 30

Now put y = 30 in Equation 1:

3x + 4 × 30 = 195
3x + 120 = 195
3x = 75 → x = 25

Step 4: Check the third statement from Assertion (A):

2 vadas and 1 samosa:
2x + y = 2 × 25 + 30 = 80

So, Assertion (A) is correct.

Step 5: Analyze Reason (R):

They define x and y correctly.

But the second equation they wrote is:
2 × 1.1x + 3 × (1/5)y = 139

This is wrong.

It should have been:
2 × 0.8x + 3 × 1.1y = 139

So, the equation in R is incorrect, even though the intent was right.

Hence, Reason (R) is false.

Conclusion:

• Assertion (A) is true
• Reason (R) is false

Final Answer: Option A