Answer

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**Hint:**To solve this question, we will use the concept of simple interest. Simple interest is the interest incurred on an amount over a certain period of time and at a nominal rate of interest. We will solve the question by substituting the given values in our formula and then find the value of the unknown term by equating it.

**Formula Used:**We will use the formula \[{\rm{Simple\, Interest = }}\dfrac{{P \times R \times T}}{{100}}\], where \[P\] is the Principal amount in Rupees that is deposited in the bank, on which the Interest is to be obtained, \[R\] is the Rate of the Interest in percentage that is given on the Principal amount, and \[T\] is the Time period in years for which the Principal amount is subjected to Interest.

**Complete step-by-step answer:**Let us now solve our question. We will first mark all the blanks in our table to ease our calculation.

Sr. No. | Principal(P) | Rate of Interest(R) | Period(N) | Interest(I) |

1. | _____(A)_____ | 6 % | 3 years | Rs. 1260 |

2. | _____(B)_____ | 7 % | 100 days | Rs. 28 |

3. | Rs. 2500 | _____(C)_____ | 2 years | Rs. 275 |

We will now solve and find the value for our blank (A).

We are provided with the following information,

Principal amount (\[P\]) = \[P\]

Rate of Interest (\[R\]) = \[6\% \]

Time Period (\[T\]) = 3 years

Simple Interest = Rs. 1260

Now we will substitute the above values in our formula for Simple Interest. On doing so we will get

\[{\rm{Simple\, Interest = }}\dfrac{{P \times R \times T}}{{100}}\]

\[1260 = \dfrac{{P \times 6 \times 3}}{{100}}\]

We will now multiply all the terms,

\[\begin{array}{l}1260 \times 100 = P \times 6 \times 3\\ \Rightarrow 126000 = P \times 18\end{array}\]

We will now divide both sides of the equation with 18. This will give us the unknown value of \[P\]. On solving we get this as follows,

\[\begin{array}{l} \Rightarrow \dfrac{{P \times 18}}{{18}} = \dfrac{{126000}}{{18}}\\ \Rightarrow P = 7000\,\,Rs.\end{array}\]

Thus, the value of our Principal Amount is 7000 Rs.

Hence, the value of blank (A) is 7000 Rs.

Similarly, we will now solve and find the value for our blank (B).

We are provided with the following information,

Principal amount (

\[P\]) = \[P\]

Rate of Interest (\[R\]) = \[7\% \]

Time Period (\[T\]) = 100 days

We require the Time period in years. Thus, we will convert our given Time Period into years.

We know that 365 days = 1 year

So, \[1\,\,day\,\, = \,\,\dfrac{1}{{365}}\,year\]

Thus, \[100\,\,day\,\, = \,\,\dfrac{{100}}{{365}}\,year\]

= \[0.274\,\,year\]

Simple Interest = Rs. 28

Now we will substitute the above values in our formula for Simple Interest. On doing so we will get

\[{\rm{Simple\, Interest = }}\dfrac{{P \times R \times T}}{{100}}\]

\[28 = \dfrac{{P \times 7 \times 0.274}}{{100}}\]

We will now multiply all the terms,

\[\begin{array}{l}28 \times 100 = P \times 7 \times 0.274\\ \Rightarrow 2800 = P \times 1.918\end{array}\]

We will now divide both sides of the equation with \[1 \cdot 918\]. This will give us the unknown value of \[P\]. On solving we get this as follows,

\[\begin{array}{l}\dfrac{{P \times 1.918}}{{1.918}} = \dfrac{{2800}}{{1.918}}\\ \Rightarrow P = {\rm{Rs}}{\rm{. }}1459.854\\ \Rightarrow P \approx {\rm{Rs}}{\rm{. }}1460\end{array}\]

Thus, the value of our Principal Amount is 1460 Rs.

Hence, the value of blank (B) is 1460 Rs.

Finally, we will now solve and find the value for our blank (C).

We are provided with the following information,

Principal amount (\[P\]) = 2500 Rs.

Rate of Interest (\[R\]) = \[R\]

Time Period (\[T\]) = 2 years

Simple Interest = Rs. 275

Now we will substitute the above values in our formula for Simple Interest. On doing so we will get

\[{\rm{Simple Interest = }}\dfrac{{P \times R \times T}}{{100}}\]

\[275 = \dfrac{{2500 \times R \times 2}}{{100}}\]

We will now multiply all the terms,

\[\begin{array}{l}275 \times 100 = 2500 \times R \times 2\\ \Rightarrow 27500 = 5000 \times R\end{array}\]

We will now divide both sides of the equation with 5000. This will give us the unknown value of \[R\]. On solving we get this as follows,

\[\begin{array}{l} \Rightarrow \dfrac{{5000 \times R}}{{5000}} = \dfrac{{27500}}{{5000}}\\ \Rightarrow R = 5.5\% \end{array}\]

Thus, the value of our Rate of Interest is \[5.5\% \].

Hence, the value of blank (C) is \[5.5\% \].

Therefore, we finally obtain our table as follows –

Sr. No. | Principal(P) | Rate of Interest(R) | Period(N) | Interest(I) |

1. | Rs. 7000 | 6 % | 3 years | Rs. 1260 |

2. | Rs. 1460 | 7 % | 100 days | Rs. 28 |

3. | Rs. 2500 | \[5.5\% \] | 2 years | Rs. 275 |

**Note:**The final amount that is obtained after the term for which the interest is provided, is given by the formula –

\[A = P\left( {1 + RT} \right)\], where, \[P\] is the Principal amount in Rupees that is deposited in the bank, on which the Interest is to be obtained, \[R\] is the Rate of the Interest in percentage that is given on the Principal amount, \[T\] is the Time period in years for which the Principal amount is subjected to Interest, and\[A\] is the Final amount in rupees that is obtained after the term of the interest is completed.

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