2023
Mathematics
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At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?
A.
15 years
B.
25 years
C.
20 years
D.
30 years
Correct Answer: 20 years
Explanation
Amount (A) = Principal (P) + Interest (I) i.e. A = P + I 1 = PTR/100 A = 3P; T = 10 years (Given) Since A = P + I ⟹3P=P+P×10×R/100 ⟹3P=P+10PR/100 ⟹3P=P+PR/10 ⟹3P−P=PR/10 ⟹2P=PR/10 ⟹2P/1=PR/10 ⟹ PR = 20P ∴ R = 20% Since the rate stays the same A = 5P; R = 20%;T =?; A =P + I ⟹5P = P + (p × T × 20)/100 ⟹5P − P = (2PT)/10 ⟹4P = (2PT)/10 ⟹2P = PT/10 ⟹ PT = 20P ∴ T = 20 years
Amount (A) = Principal (P) + Interest (I) i.e. A = P + I 1 = PTR/100 A = 3P; T = 10 years (Given) Since A = P + I ⟹3P=P+P×10×R/100 ⟹3P=P+10PR/100 ⟹3P=P+PR/10 ⟹3P−P=PR/10 ⟹2P=PR/10 ⟹2P/1=PR/10 ⟹ PR = 20P ∴ R = 20% Since the rate stays the same A = 5P; R = 20%;T =?; A =P + I ⟹5P = P + (p × T × 20)/100 ⟹5P − P = (2PT)/10 ⟹4P = (2PT)/10 ⟹2P = PT/10 ⟹ PT = 20P ∴ T = 20 yearsTHIS WEEK's
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