Multiple choice

The difference between the compound interest and the simple interest earned on a sum of money at the end of $4$ years is $Rs.256.40$. find the sum . Which of the following information given in the statements P and Q is / are necessary P: Amount of simple interest after $4$ years Q: Rate of interest per annum

  1. Only P is necessary

  2. Only Q is necessary

  3. Both P & Q are necessary

  4. Neither of P & Q are necessary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between CI and SI for 2 years is P(r/100)^2. For 4 years, the formula is more complex, involving the rate r. Without the rate, the difference cannot be used to find the sum P, even if SI is known. Thus, Q is necessary.

AI explanation

The formula for the difference between compound interest and simple interest for 4 years is Difference = P times (R/100) to the fourth power plus 4 times P times (R/100) cubed divided by 100 plus 6 times P times (R/100) squared divided by 100 squared. To solve for the principal P using the given difference of Rs. 256.40, the rate of interest R is strictly required. Once P is found using the rate from statement Q, the simple interest can be easily calculated, making statement P unnecessary. Therefore, only Q is necessary.

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