A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. What is the value of the item's custom duty and sales tax?

Question: A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. What is the value of the item's custom duty and sales tax?

Solution:
Let the value of the baggage items be x.

Customs duty = 50% of x = 0.5x

Total value including customs duty = x + 0.5x = 1.5x

Sales tax = 20% of (total value + customs duty already paid)
∴ Sales tax = 20% of 1.5x
= (20/100) × 1.5x
= 0.2 × 1.5x
= 0.3x

According to the question, total tax (customs duty + sales tax) = 350
∴ 0.5x + 0.3x = 350
⇒ 0.8x = 350
⇒ x = 350/0.8
⇒ x = 437.5

Now, the total value of customs duty and sales tax is already given in the question as Tk. 350.
Total tax = 0.8x = 0.8 × 437.5 = 350

Since the question asks "What is the value of the item's custom duty and sales tax?" and it is given as 350, we look for 350 in the options.

সঠিক উত্তর: ঘ) None

বিঃদ্রঃ এই প্রশ্নটি ভাষাগত একটু অস্পষ্টতা রয়েছে। কারণ, "What is the value of the item's custom duty and sales tax?" এই তথ্য প্রশ্নেই "The total custom duty and sales tax is Tk. 350" হিসেবে দেয়া আছে। সম্ভবত প্রশ্নে উদ্দেশ্য ছিলো “What is the value of the items?” এর মান বের করা। সেক্ষেত্রেও, Value of the items = Tk. 437.5 হবে। এবং উত্তর হবে ঘ) None