a) ₹ 1580

b) ₹ 2400

c) ₹ 2800

d) none of these.

correct answer is: b) ₹ 2400

**Explanation**

Here, ‘Sum’ means ‘Principal’.

Rate = 3\frac{3}{4} % or \frac{15}{4} %

Time = 2\frac{1}{3} years or \frac{7}{3} years

Simple interest = ₹ 210

Let, Principal = ‘p’

We know, S.I. =\frac{p\ \times\ r\ \times\ t}{100}

\therefore₹210=\left(\frac{p\times15\times7}{100\times4\times3}\right) _{[put the value]}

\rightarrow₹210=\left(\frac{105p}{1200}\right)

\rightarrow\ 105p = ₹ 252000 _{[cross multiply]}

\rightarrow\;p=₹\left(\frac{252000}{105}\right)

\rightarrow\ p = ₹ 2400

\therefore The sum will be ₹ 2400 .**Ans:** The sum will be ₹ 2400 .

**Another form of this specific question is:****1.** Calculate the principal sum at which the simple interest, at a rate of 3 ¾% per annum, amounts to ₹210 in 2 1/3 years.**2.** Determine the sum at which the simple interest becomes ₹210 in 2 1/3 years with an interest rate of 3 ¾% per annum.**3.** Find the principal amount for which the simple interest, at a 3 ¾% per annum rate, is ₹210 over a period of 2 1/3 years.**4.** Calculate the initial amount needed for the simple interest, at a rate of 3 ¾% per annum, to be ₹210 within 2 1/3 years.**5.** In what principal sum will the simple interest be ₹210 over 2 1/3 years at a rate of 3 ¾% per annum?