Question

A. THE DIFFERENCE BETWEEN COMPOUND INTEREST AND SIMPLE INTEREST ON A SUM OF RS 3000 FOR 3 YEARS IS RS 93.THE RATE PERCENT PER ANNUM IS?

Answer 1

Let Interest be I   
   Principle= P=3000, time =t=3 and rate of interest=r
Then  for C I=P(1+r)³-P =3000(1+r)³-3000
For simple interest S I= P*r*t= 3000*3*r
we have 3000(1+r)³-3000- 9000r=93
         ⇒ 3000+3000r³+9000r²+9000r-3000-9000r=93
         ⇒ 3000r³+9000r²-93=0
         ⇒ 3000r³ -300r²+9300r²-93=0
         ⇒ 300r²(10r-1)+93(100r²-1)=0
         ⇒ 300r²(10r-1)+93 (10r+1)(10r-1)=0
         ⇒ (10r-1)(300r²-930r-93)=0
       solving  we have 10r-1=0 or r=1/10=10%
Hence interest rate is 10%

Answer 2

P(1+r)³ - P - P r 3 = 93

 r³ + 3 r² + 3 r + 1 - 1 - 3 r = 93 /3000

r³ + 3 r² = 0.031

r is a fraction, like 10% or 0.1, so r³ is much smaller than r².  Neglect r³ term.
     r² ≈ 0.031 /3
      r ≈ 0.101653
 Let  us try r = 0.1  or 10% per annum.

   0.1³ + 3 0.1² = 0.031  =>      r = 10%

You can also use the standard cubic equation solution methods to find answer.