The cost of item A is 40% more than that of item B and the cost of item B is 25% less than that of item C. The cost of A is decreased by 20%, while that of B and C are increased by 24% and 33%, respectively.

Statement I: The total new cost of items A, B and C is 24% less than the total initial cost of 2B and C.

Statement II: The total new cost of A and 2B is $$33\frac{1}{3}$$​% more than the total initial cost of A and B.

Which of the above statements is/are correct?

Correct option is B

Given:
Let the initial cost of item C = ₹100 (for simplicity)
Cost of item B = 25% less than C = ₹100 – ₹25 = ₹75
Cost of item A = 40% more than B = ₹75 + 40% of ₹75 = ₹105
Formula Used:
Percentage change = $$\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$$​​
Solution:

Now apply percentage changes:
A decreases by 20% → New A = ₹105 – 20% of ₹105 = ₹84
B increases by 24% → New B = ₹75 + 24% of ₹75 = ₹93
C increases by 33% → New C = ₹100 + 33% of ₹100 = ₹133
Statement I: The total new cost of items A, B and C is 24% less than the total initial cost of 2B and C.
New total = A + B + C = ₹84 + ₹93 + ₹133 = ₹310
2B + C (initial) = 2 × ₹75 + ₹100 = ₹250
% Change = $$\frac{310 - 250}{250} \times 100 = 24$$​ increase, not decrease
So, Statement I is incorrect
Statement II: The total new cost of A and 2B is $$33\frac{1}{3}$$​% more than the total initial cost of A and B.
New cost of A + 2B = ₹84 + 2×₹93 = ₹84 + ₹186 = ₹270
Initial cost of A + B = ₹105 + ₹75 = ₹180
% change = $$\frac{270 - 180}{180} \times 100 = \frac{90}{180} \times 100 = 50\%$$​​
Not 33⅓%, so Statement II is incorrect
Thus, the correct option is (b)  Neither I nor II