Step 1: Set up the initial linear equation

Let the original cost of one orange be $x$ and one banana be $y$. Arnab buys 9 oranges and 8 bananas for ₹276.

$9x + 8y = 276$

Step 2: Set up the second equation with the decreased price

The cost of an orange decreases by 10%, making the new cost $0.9x$. The cost of 5 oranges and 10 bananas is ₹210.

$5(0.9x) + 10y = 210 \implies 4.5x + 10y = 210$

Step 3: Solve the system of linear equations

Multiply the second equation by 2 to match the coefficient of $y$: $9x + 20y = 420$. Subtract the first equation ($9x + 8y = 276$) from this:

$12y = 144 \implies y = 12$

Step 4: Find the cost of an orange ($x$)

Substitute $y = 12$ into the first equation $9x + 8(12) = 276$:

$9x + 96 = 276 \implies 9x = 180 \implies x = 20$

Step 5: Calculate the original cost of 4 oranges and 3 bananas

Substitute $x = 20$ and $y = 12$ into the target expression $4x + 3y$:

$4(20) + 3(12) = 80 + 36 = 116$