The difference between the compound interest and simple interest on a certain sum of money at 20/3% per annum for 3 years is rupees to 46.Find the sum.
Answers
Let the sum be P
Given: R= 20/3% and T=3 yrs
Therefore, S.I.= PRT/100
=(P×20/3×3)/100
=P×1/5 = 1/5P
Now, C.I.= P(1+R/100)^n. - P
=P(1+20/3/100)^3 - P
=P(1+20/300)^3 - P
=P((300+20)/300)^3 - P
=P(320/300)^3 - P
=P(16/15)^3 - P {On cancelling 320 and 300 to get 16 and 15}
=P×16/15×16/15×16/15
=P×4096/3375
= 4096/3375P - P
=(4096-3375)/3375 P
= 721/3375P
ATQ,
C.I. - S.I. = ₹46
i.e. ₹(721/3375 - 1/5)P = ₹46 implies that₹((721-675)/3375)P=₹46
implies that₹(46/3375)P = ₹46
implies that P = ₹(46×3375)/46
implies that P = ₹3375 {Ans}
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