Vedic Age

Most students learn the Simple Interest formula, then panic when the exam asks about the Amount, the Principal, or about money "doubling" and "tripling". The trick is to see that these are all the same idea wearing different costumes — and once you fix Principal = 100 as your mental base, the entire chapter collapses into one-step mental math.

Definition: Simple Interest (SI) is the interest charged only on the original principal, never on accumulated interest. Formula: SI = (P × R × T) / 100.

Definition: Amount (A) is the total money repaid at the end — principal plus interest. A = P + SI, which expands to A = P[1 + (RT/100)].

From SI to Amount: just add the principal back

When a question says "what will Rs 8,000 become at 12% SI for 5 years?", it is asking for A, not SI. Build the answer in two strokes:

• SI = 8000 × 12 × 5 / 100 = Rs 4,800.
• A = P + SI = 8,000 + 4,800 = Rs 12,800.

The compact form A = P[1 + (RT/100)] gives the same number in one breath: 8000 × [1 + (12×5)/100] = 8000 × 1.6 = Rs 12,800. Use whichever feels faster on the day.

From Amount back to Principal — the inverse formula

If you know the Amount A and need P, do not solve a fresh equation under exam pressure. Use the rearrangement directly:

P = (100 × A) / (100 + RT)

Why? Start from A = P × (100 + RT)/100, cross-multiply, and the formula falls out. Memorise it as a shape: "100 times A on top, 100 plus RT on bottom". For example, if a sum becomes Rs 6,000 in 4 years at 5% SI, then P = (100 × 6000) / (100 + 20) = 6,00,000 / 120 = Rs 5,000.

The "becomes n times" pattern — every exam tests this

Big idea: if a sum becomes n times itself in T years at simple interest, then the interest earned equals (n − 1) times the principal, so:

n − 1 = (R × T) / 100

That single relation answers every "doubles / triples / quadruples in how many years / at what rate" question.

Worked example.

Question: At what rate of simple interest will a sum of money double itself in 8 years?

Solution:
Step 1: Doubling means n = 2, so n − 1 = 1.
Step 2: Apply 1 = (R × 8)/100.
Step 3: R = 100 / 8 = 12.5%.

Conclusion: The sum doubles at 12.5% per annum SI.

Another quick one. If money triples (n = 3), the interest earned = 2 × Principal. So 2 = (R × T)/100, giving RT = 200. At 10% SI, T = 20 years; at 20% SI, T = 10 years. The two unknowns are linked by a single product — fix one, the other falls out.

Why setting Principal = 100 makes you fast

Percentage problems are silently asking "for every 100 rupees, what happens?". If you assume P = 100, then SI is literally just R × T (because dividing by 100 is identity). At 10% for 3 years, SI = 30, so A = 130. A sum that becomes 1.5 times means A = 150 on P = 100, so SI = 50; if T = 5, then R = 10%. No formula manipulation, just arithmetic on a scale of 100. Indian exam toppers default to this because it shaves five to ten seconds off every problem — and you have only about 45 seconds per question in IBPS- or RPF-style speed sections.

Why it matters: RPF Constable, SSC, RRB NTPC and banking prelims rarely ask for raw SI on a fixed sum. They ask for the Principal, the Amount, the time to double, or the rate that triples a sum. All four patterns sit on top of the SI base relation — so mastering this lesson covers maybe one in every six arithmetic questions in those papers.

Real-world example

A family loans Rs 25,000 to a relative at 9% SI for 4 years. Use A = P[1 + RT/100] = 25,000 × [1 + 0.36] = 25,000 × 1.36 = Rs 34,000. They are repaid Rs 34,000 — Rs 9,000 of interest. The same logic shows up on every Indian Post Office NSC certificate, on Kisan Vikas Patras, and on government bond yield calculations during quick mental cross-checks.

Common misconception

Aspirants sometimes treat "money doubles" as "interest rate = 100%". That confuses the target amount (which is twice the principal) with the rate of interest (which is the per-year percentage). The correct link is n − 1 = RT/100. Money doubling does not mean R = 100; it means the product RT equals 100. R could be 10% with T = 10 years, or 12.5% with T = 8 years — the combination matters, not either number alone.

One more worked example — going backwards

Question: A sum of money amounts to Rs 9,600 in 5 years and to Rs 11,200 in 8 years at simple interest. Find the rate and the principal.

Solution:
Step 1: SI for 3 years (from year 5 to year 8) = 11,200 − 9,600 = Rs 1,600. So SI per year = Rs 533.33.
Step 2: SI for 5 years = 5 × 533.33 = Rs 2,666.67. So P = 9,600 − 2,666.67 = Rs 6,933.33.
Step 3: Rate = (SI × 100)/(P × T) = (2,666.67 × 100)/(6,933.33 × 5) ≈ 7.69%.

Conclusion: Principal ≈ Rs 6,933 and rate ≈ 7.69% per annum. The clean trick here is "two amounts at two times → subtract to isolate yearly interest" — a standard SBI/IBPS pattern.

Four Vedas (Samhitas): RIG (oldest, 1028 hymns, 10 mandalas — Mandala III has the Gayatri Mantra to Savitri/Sun by Vishwamitra), SAMA (melodies/music — origin of Indian music), YAJUR (sacrificial formulae/prose), ATHARVA (charms, spells, magic — latest, folk traditions). Mnemonic 'R-S-Y-A: Recite, Sing, Yajna, Atharva-magic'. Each Veda has Brahmanas (ritual prose), Aranyakas (forest texts/philosophy), and Upanishads (Vedanta — philosophy, 108 in number, Mundaka Upanishad gives 'Satyameva Jayate'). The Vedangas (6 limbs: Shiksha, Kalpa, Vyakarana, Nirukta, Chhanda, Jyotisha) aid Veda study. 'Aa No Bhadra' and other hymns reflect Rig Vedic worldview.

Rig Vedic gods were nature-based: INDRA (most hymns, war/rain, 'Purandara'=fort-destroyer), AGNI (2nd most, fire, intermediary), VARUNA (cosmic order/Rita), Soma (plant/drink). Later Vedic prominence shifted to Prajapati (creator), Rudra, Vishnu. The Purusha Sukta (Rig Veda 10th Mandala) first mentions the four varnas. Polity: King (Rajan) aided by Purohita, Senani, Gramani; the Sabha and Samiti were key assemblies (women attended Sabha in early period). Later Vedic kings performed Rajasuya (coronation), Ashvamedha (horse sacrifice), Vajapeya (chariot race) to assert power. Position of women declined in the Later Vedic age.

Cover the answer, recall, then check. 12 cards on the must-know facts for UPSC Prelims.

Q1. Distinguish the Early (Rig Vedic) and Later Vedic periods by date.
A1. Early/Rig Vedic c. 1500–1000 BCE (Punjab–Saptasindhu); Later Vedic c. 1000–600 BCE (shift eastward to Ganga-Yamuna doab).

Q2. Name the four Vedas and their nature.
A2. Rigveda (hymns, oldest), Samaveda (melodies/music), Yajurveda (sacrificial formulae), Atharvaveda (spells/charms). Collectively "Samhitas".

Q3. What is the correct order of Vedic literature after the Samhitas?
A3. Samhitas → Brahmanas (ritual prose) → Aranyakas ("forest texts") → Upanishads (philosophy/Vedanta).

Q4. Which Rigvedic hymn (Purusha Sukta) mentions the four varnas, and in which Mandala?
A4. The Purusha Sukta in the 10th Mandala of the Rigveda — the only Rigvedic reference to the four-fold varna system.

Q5. Where is the Gayatri Mantra found and to whom is it addressed?
A5. In the Rigveda (3rd Mandala), composed by sage Vishvamitra, addressed to Savitri (the Sun god).

Q6. What was the chief deity of the Rigveda, and which deities rose in importance later?
A6. Indra (war/rain) was most invoked, then Agni and Varuna. In Later Vedic times Prajapati, Vishnu and Rudra (Shiva) gained prominence.

Q7. Name the key political assemblies of the Vedic polity.
A7. Sabha (elders/council), Samiti (general assembly), Vidatha (earliest, multi-purpose), Gana. The king was "Rajan".

Q8. What was the main economic basis of Rig Vedic vs Later Vedic society?
A8. Rig Vedic: pastoral, cattle-centred (wealth = "gomat"; cattle = "gau"). Later Vedic: settled agriculture with iron ("krishna ayas") ploughs.

Q9. Which four great sacrifices marked Later Vedic kingship?
A9. Rajasuya (royal consecration), Ashvamedha (horse sacrifice), Vajapeya (chariot race), and elaborate soma rituals — signalling growing royal power.

Q10. What are the four ashramas and four purusharthas of Vedic-derived tradition?
A10. Ashramas: Brahmacharya, Grihastha, Vanaprastha, Sannyasa. Purusharthas: Dharma, Artha, Kama, Moksha.

Q11. What is the meaning of "Aryan" as used in the Rigveda and the famous "Battle of Ten Kings"?
A11. "Arya" meant noble/kinsmen, not a race. The Dasarajna (Battle of Ten Kings) on the Parushni (Ravi) saw Sudas of the Bharata (Tritsu) win.

Q12. Which national motto comes from Vedic literature and its source?
A12. "Satyameva Jayate" (Truth alone triumphs) is from the Mundaka Upanishad.

Worked Example

Problem/Question: Consider the following pairs of Vedic terms and their meanings:

1. Sabha — assembly of elders/nobles
2. Samiti — larger assembly of the whole people (folk)
3. Vidatha — a purely military war-council
   How many of the pairs are correctly matched?
   (a) Only one (b) Only two (c) All three (d) None

Solution/Model answer:

• Pair 1: In the Rig Vedic polity, the Sabha was a smaller, more select assembly of elders and prominent men. Correctly matched.
• Pair 2: The Samiti was the larger folk assembly that even elected/discussed the rajan (king). Correctly matched.
• Pair 3: Vidatha was the earliest and most versatile assembly, associated with distribution of spoils, religious, social and economic functions — not a "purely military war-council." Incorrectly matched.
  Two pairs (1 and 2) are correct. Eliminate (c) all three and (d) none; between (a) one and (b) two, since both Sabha and Samiti are right, the answer is two.

Answer/Takeaway: (b) Only two.