Arpita buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 3 oranges and 4 bananas?

Correct option is A

Given:

Cost of 9 oranges and 8 bananas = ₹276.

After a 10% decrease in the cost of an orange and the cost of bananas remaining the same, the cost of 5 oranges and 10 bananas = ₹210.

Solution:

The cost of one orange = ₹x and the cost of one banana = ₹y.

From the first condition:

9x + 8y = 276............*(1)

From the second condition:

Cost of one orange after a 10% decrease = 0.9x.

Therefore, the cost of 5 oranges = 5 \times 0.9x = 4.5x.

Cost of 10 bananas = 10y.

Thus, the total cost = 4.5x + 10y = 210...............(2)

On solving (1) and (2)

Multiply Equation 2 by 2 to eliminate the decimal:

2(4.5x + 10y) = 2(210)

9x + 20y = 420

Now subtract Equation 1 from Equation 3:

9x + 20y - (9x + 8y) = 420 - 276

12y = 144

y =$$\frac{144}{12} = 12$$​​

Substitute y = 12 in Equation 1:

9x + 8(12) = 276

9x + 96 = 276

9x = 276 - 96

9x = 180

x =$$\frac{180}{9} = 20$$​​

Cost of 3 oranges = 3x =$$3 \times 20$$​ = 60.

Cost of 4 bananas = 4y = $$4 \times 12$$​ = 48.

Total cost = 60 + 48 = 108.