Correct Answer - Option 1 : (10/3)%
Given:
Principal becomes 6/5 of itself in 6 years.
Concepts used:
S.I. (Simple interest) = (P × R × T)/100
P → Principal,
R → Rate of interest per annum,
T → Time (in years)
Amount = Principal + S.I.
Calculation:
Let the sum of money lent (Principal) be Rs. x.
S.I. (Simple interest) = (P × R × T)/100
⇒ S.I. = x × R × 6/100
⇒ 6xR/100
Amount = Principal + S.I.
⇒ 6/5 of x = x + (6xR/100)
⇒ (6/5)x – x = 6xR/100
⇒ x/5 = 6xR/100
⇒ R = 100/(5 × 6) % p.a.
⇒ R = (10/3) %
∴ The rate of interest earned is (10/3) % p.a.
Let principal = X, A = 3X, T = 8 years, R = ?
Case I,
`"A" = "P"[ 1 + "R"/100 ]^"T"`
`"3X" = "X"[ 1+ "R"/100 ]^8`
`3^(1/8) = 1 + "R"/100 ` ...(1)
Case II,
P = X, A = 27X, T = ?
`27"X" = "X"[ 1 + "R"/100 ]^"T"`
`27^(1/T) = 1 + "R"/100` ...(2)
From (1) and (2)
`3^(1/8) =
27^(1/T)`
`3^(1/8) = 3^(1/8) = 3/"T"`
T = 24
Time = 24 years.
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A certain sum becomes 3 times ...
Updated On: 27-06-2022
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Answer : B
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