Mathematics for FinancePYQ June 19Question 1189 of 512
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The certain sum of money became Rs. 692\displaystyle \text{Rs. }692 in 2\displaystyle 2 years and Rs. 800\displaystyle \text{Rs. }800 in 5\displaystyle 5 years then the principal amount is

Options

ARs. 520\displaystyle \text{Rs. }520
BRs. 620\displaystyle \text{Rs. }620
CRs. 720\displaystyle \text{Rs. }720
DRs. 820\displaystyle \text{Rs. }820
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Correct Answer

✅ Option b — Rs. 620\displaystyle \text{Rs. }620

All Options:

  • ARs. 520\displaystyle \text{Rs. }520
  • BRs. 620\displaystyle \text{Rs. }620
  • CRs. 720\displaystyle \text{Rs. }720
  • DRs. 820\displaystyle \text{Rs. }820

Detailed Solution & Explanation

**Derivation of Principal under Simple Interest** Given: - Amount after 2\displaystyle 2 years (A2\displaystyle A_2) = Rs. 692\displaystyle \text{Rs. }692 - Amount after 5\displaystyle 5 years (A5\displaystyle A_5) = Rs. 800\displaystyle \text{Rs. }800 **Step 1: Find Simple Interest per year (I\displaystyle I)** Simple Interest remains constant each year: Interest for 3 years (5−2)=A5−A2=800−692=Rs. 108\text{Interest for } 3 \text{ years } (5 - 2) = A_5 - A_2 = 800 - 692 = \text{Rs. }108 Interest per year (I)=1083=Rs. 36\text{Interest per year } (I) = \frac{108}{3} = \text{Rs. }36 **Step 2: Find the Principal (P\displaystyle P)** Using the amount equation for 2\displaystyle 2 years: A2=P+2IA_2 = P + 2I 692=P+2(36)692 = P + 2(36) 692=P+72692 = P + 72 P=692−72=Rs. 620P = 692 - 72 = \text{Rs. }620 Hence, **Option B** is the correct answer.

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