Answer: Option B
Let the three parts into which Rs 9400 is to be divided be x, y, and z respectively.The given rate of interest is 5% per annum.The formula to calculate simple interest is:Simple Interest (S.I.) = (P × R × T) / 100Where, P is the principal amount, R is the rate of interest, and T is the time period in years.Given that the simple interest on the three parts after 3, 4, and 5 years are equal. This implies thatx × 5 × 3 = y × 5 × 4 = z × 5 × 515x = 20y = 25zDividing the given amount of Rs 9400 into three parts, we havex + y + z = 9400Using the ratio we found above, we getz = (15/25) (x + y + z) = (3/5) (x + y + z)Substituting the value of z in the equation above, we get15x = 20y = (5/3)z(x + y + z)15x = 20y = (5/3)(3x + 3y + 5z)15x = 20y = 9x + 9y + 25zSimplifying the above equation, we get6x = 5y - 25zBut we know that z = (3/5) (x + y + z)Substituting the value of z, we get6x = 5y - 25(3/5)(x + y)6x = 5y - 15x - 15y21x = 20yx/y = 20/21Let the sum x be the smallest. Then, we havex = (20/21)(x + y + z)x = (20/21) (9400)x = 2400Therefore, the smallest part is Rs 2400, which is option B.