The cost of a motorbike is 75% less than the cost of a car. The cost of a car decreases by 25% and that of a motorbike increases by 40%.

Statement I:  The new cost of motorbike is 53$$\frac{1}{3}$$​​% less than new cost of car?​

Statement II: The total new cost of one car and two motorbikes is 3$$\frac{1}{3}$$​% more than their total initial cost. ​

Which of the above statements is/are correct?

Correct option is C

Given:

• Initial cost of motorbike is 75% less than that of a car.
  That means:
  If car = ₹100, then motorbike = ₹25
• Car decreases by 25% → New cost of car = ₹100 − ₹25 = ₹75
• Motorbike increases by 40% → New cost = ₹25 + 40% of ₹25 = ₹25 + ₹10 = ₹35

Statement I:

Is the new cost of motorbike 53$$\frac{1}{3}$$​% less than new cost of car?

New cost of car = ₹75
New cost of bike = ₹35

Let’s find the % decrease of bike w.r.t car:

​$$\text{Percentage less} = \frac{75 - 35}{75} \times 100 = \frac{40}{75} \times 100 = 53.\overline{3}\%$$

So, Statement I is correct

Statement II:

Compare total new cost vs total old cost for 1 car + 2 bikes

Initial total cost:

• 1 car = ₹100
• 2 motorbikes = ₹25 × 2 = ₹50
  → Total initial = ₹150

New total cost:

• 1 car = ₹75
• 2 motorbikes = ₹35 × 2 = ₹70
  → Total new = ₹145

Now find % change: 

​$$\text{Change} = \frac{145 - 150}{150} \times 100 = \frac{-5}{150} \times 100 = -3.\overline{3}\%$$

So it is not 3$$\frac{1}{3}$$​% more, it is actually 3.33% less

Statement II is incorrect

Final Answer: (C) I only​​

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