Seven chairs and three tables together cost ₹7400, three chairs and five tables together cost ₹5400. The total cost (in ₹) of 1 chair and 2 tables is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2000
Let the cost of a chair = x and cost of a table = y.
We are given:
- $7x + 3y = 7400$
- $3x + 5y = 5400$
We need cost of 1 chair + 2 tables = $x + 2y$.
Step 1: Solve the system of equations
From equation 1:
$7x + 3y = 7400$
From equation 2:
$3x + 5y = 5400$
Step 2: Multiply equations to eliminate $x$
- Multiply eqn 1 by 3: $21x + 9y = 22200$
- Multiply eqn 2 by 7: $21x + 35y = 37800$
Subtract first from second:
$(21x + 35y) - (21x + 9y) = 37800 – 22200$
$26y=15600 ⟹ y=600$
Step 3: Find $x$
$3x+5(600)=5400 ⟹ 3x+3000=5400$
$3x=2400 ⟹ x=800$
Step 4: Find $x + 2y$
$x + 2y = 800 + 2 \cdot 600 = 2000$