Question

According to the decimal place-value system (Dashagunanika) used in Indian mathematics, identify the correct numerical equivalents for the following terms:
A. Sahasram = 1,000
B. Abjam = 100,000
C. Laksham = 100,000
D. Prayutam = 1,000,000
E. Koti = 1,000,000

• A. Only A, C, D
• B. Only B, C, D
• C. Only D, E, A
• D. Only A, B, C

Hint:

The Indian system goes by powers of 10. Eka(1) $\rightarrow$ Dasha(10) $\rightarrow$ Shata(100) $\rightarrow$ Sahasra(1,000) $\rightarrow$ Ayuta(10,000) $\rightarrow$ Laksha(100,000) $\rightarrow$ Prayuta(1,000,000) $\rightarrow$ Koti(10,000,000).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Indian mathematics developed the base-10 place value system. In works like Lilavati, names are given to powers of 10 up to very high values (e.g., Eka, Dasha, Shata, Sahasra, Ayuta, Laksha, Prayuta, Koti, etc.).

Step 2: Detailed Explanation of Terms:
1. Sahasram (A): Means one thousand ($10^3$). Statement (A) is TRUE.
2. Abjam (B): 'Abja' usually refers to a 'Padma' or 'Arbuda', which signifies a much larger number (often $10^9$ or $1,000,000,000$). Using it for 100,000 is incorrect in the standard series. Statement (B) is FALSE.
3. Laksham (C): Means one lakh, which is exactly one hundred thousand ($10^5$). Statement (C) is TRUE.
4. Prayutam (D): In the standard sequence (Eka, Dasha, Shata, Sahasra, Ayuta, Laksha, Prayuta), 'Prayuta' follows Laksha and means one million ($10^6$). Statement (D) is TRUE.
5. Koti (E): Means ten million ($10^7$). The prompt's OCR says 1,000,000 (which is Prayuta). Therefore, Statement (E) is FALSE.

Step 3: Verification with Options:
- The true numerical pairs are Sahasra (1,000), Laksha (100,000), and Prayuta (1,000,000).
- Option (1) identifies this set: "Kevalam A, C, D".

Step 4: Final Answer:
The correct numerical equivalents are A, C, and D.