Question
Download Solution PDFIf at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹51, then what is the principal (in ₹)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
SI = ₹42
CI = ₹51
Time (T) = 2 years
Formula Used:
SI = (P × R × T) / 100
CI = P (1 + R/100)T - P
Calculation:
42 = (P × R × 2) / 100
⇒ PR = 42 × 50
⇒ PR = 2100 ...(1)
51 = P (1 + R/100)2 - P
⇒ 51 = P [(1 + R/100)2 - 1]
⇒ 51 = P [1 + 2R/100 + (R/100)2 - 1]
⇒ 51 = P [R/50 + R2/10000]
⇒ 510000 = P [200R + R2]
⇒ 510000 = 200PR + PR2 ...(2)
Substitute (1) in (2):
⇒ 510000 = 200 × 2100 + 2100 × R
⇒ 510000 = 420000 + 2100R
⇒ 90000 = 2100R
⇒ R = 90000 / 2100
⇒ R = 300 / 7
Substitute R in (1):
⇒ P × (300 / 7) = 2100
⇒ P = 2100 × (7 / 300)
⇒ P = 7 × 7 = 49
∴ The correct answer is Option (3).
Last updated on Jun 6, 2025
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