57. Question given below is followed by two Statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer
The difference between the compound interest and the simple interest earned on a sum of money at same rate of interest for 3 yr. is '76.25. What is the sum?
I. The simple interest earned in 3 yr is '15000.
II. Rate of interest per annum is 5%
Let P = Principal R = Rate of interest (%) r = (R/ 100)
[P(1+r)^3 -P] - 3 Pr = 76.25
From statement I, 3 Pr = 1500
Pr = 500
Hence, from Eq. (i) and (ii), we get [P(1+r)³ -P] - 3 pr = 76.25
[P(1+r^3+3r(1+r)-P)] - 3Pr = 76.25
Pr (r² + 3r) = 76.25
r² + 3r = 76.25/ 500 One root is +Ve, While the other is - Ve Hence, r can be found. This implies, P can be found, statement I is sufficient.
From statement II alone ⇒ r = 5/100
Thus, from eg (i)
[P(1.05)^3 -P]-(3p) (100) = 76.25 Hence, P can be found, So, statement II is sufficient.
Let P = Principal R = Rate of interest (%) r = (R/ 100)
[P(1+r)^3 -P] - 3 Pr = 76.25
From statement I, 3 Pr = 1500
Pr = 500
Hence, from Eq. (i) and (ii), we get [P(1+r)³ -P] - 3 pr = 76.25
[P(1+r^3+3r(1+r)-P)] - 3Pr = 76.25
Pr (r² + 3r) = 76.25
r² + 3r = 76.25/ 500 One root is +Ve, While the other is - Ve Hence, r can be found. This implies, P can be found, statement I is sufficient.
From statement II alone ⇒ r = 5/100
Thus, from eg (i)
[P(1.05)^3 -P]-(3p) (100) = 76.25 Hence, P can be found, So, statement II is sufficient.
Let P = Principal R = Rate of interest (%) r = (R/ 100)
[P(1+r)^3 -P] - 3 Pr = 76.25
From statement I, 3 Pr = 1500
Pr = 500
Hence, from Eq. (i) and (ii), we get [P(1+r)³ -P] - 3 pr = 76.25
[P(1+r^3+3r(1+r)-P)] - 3Pr = 76.25
Pr (r² + 3r) = 76.25
r² + 3r = 76.25/ 500 One root is +Ve, While the other is - Ve Hence, r can be found. This implies, P can be found, statement I is sufficient.
From statement II alone ⇒ r = 5/100
Thus, from eg (i)
[P(1.05)^3 -P]-(3p) (100) = 76.25 Hence, P can be found, So, statement II is sufficient.