Multiple choice

Three sums P1, P2 and P3 are such that P2 is simple interest of P1 and P3 is simple interest of P2. If in both the conditions time and rate of interest are same then find a relation between P1, P2 and P3 तीन धनराशियां P1, P2 और P3 ऐसी है कि P1, P2 पर साधारण ब्याज है और P3, P2 पर साधारण ब्याज है। यदि दोनों स्थितियों में समय और ब्याज दर समान है तो P1, P2 और P3 में सम्बन्ध ज्ञात कीजिए।

  1. P32 = P1, P2

  2. P12 = P1, P3

  3. P22 = P1, P3

  4. P2 = P1, P3

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C Correct answer
Explanation

Given P2 is SI on P1 and P3 is SI on P2 with same rate R and time T: P2 = P1 × R × T / 100 and P3 = P2 × R × T / 100. Multiplying: P2 × P3 = P1 × P2 × (R × T / 100)^2. Dividing by P2: P2 × P3 = P1 × P2 × k, which simplifies to P2² = P1 × P3.