A certain sum amounts to 15,748 in 3 years at simple interest at 1% p.a. The same sum amounts to 16,510 at r+2% p.a. SI in the same time. What is the value of r ?

Option b: 8%. Solution: Derivation of Rate of Simple Interest Given: - Amount at r% simple interest in 3 years ( A1 ) = Rs. 15,748 - Amount at (r+2)% simple interest in 3 years ( A2 ) = Rs. 16,510 Step 1: Express the difference in amounts The difference in the two amounts is due to the additional simple interest earned from the increase in rate by 2% . Additional Simple Interest = A2 - A1 = 16510 - 15748 = Rs. 762 Step 2: Find the Principal ( P ) using the additional simple interest Additional SI = × Additional Rate × t100 762 = P × 2 × 3/100 762 = 6P/100 6P = 76200 P = Rs. 12,700 Step 3: Solve for the rate of interest ( r ) Using the simple interest earned in the first case: SI1 = A1 - P = 15748 - 12700 = Rs. 3,048 SI1 = P × r × t/100 3048 = 12700 × r × 3/100 3048 = 381 r r = 3048/381 = 8% per annum Hence, Option B is the correct answer.

A certain sum amounts to $15,748$ in $3$ years at simple interest at $1\%$ p.a. The same sum amounts to $16,510$ at $r+2\%$ p.a. SI in the same time. What is the value of $r$?

The correct answer is Option b: $8\%$. **Derivation of Rate of Simple Interest** Given: - Amount at $r\%$ simple interest in $3$ years ($A_1$) = $\text{Rs. }15,748$ - Amount at $(r+2)\%$ simple interest in $3$ years ($A_2$) = $\text{Rs. }16,510$ **Step 1: Express the difference in amounts** The difference in the two amounts is due to the additional simple interest earned from the increase in rate by $2\%$. $$\text{Additional Simple Interest} = A_2 - A_1 = 16510 - 15748 = \text{Rs. }762$$ **Step 2: Find the Principal ($P$) using the additional simple interest** $$\text{Additional SI} = \frac{P \times \text{Additional Rate} \times t}{100}$$ $$762 = \frac{P \times 2 \times 3}{100}$$ $$762 = \frac{6P}{100}$$ $$6P = 76200 \implies P = \text{Rs. }12,700$$ **Step 3: Solve for the rate of interest ($r$)** Using the simple interest earned in the first case: $$SI_1 = A_1 - P = 15748 - 12700 = \text{Rs. }3,048$$ $$SI_1 = \frac{P \times r \times t}{100}$$ $$3048 = \frac{12700 \times r \times 3}{100}$$ $$3048 = 381 r \implies r = \frac{3048}{381} = 8\% \text{ per annum}$$ Hence, **Option B** is the correct answer.

Mathematics of FinanceMCQPYQ July 21Question 1225 of 512

All Questions

A certain sum amounts to $\displaystyle 15,748$ in $\displaystyle 3$ years at simple interest at $\displaystyle 1\%$ p.a. The same sum amounts to $\displaystyle 16,510$ at $\displaystyle r+2\%$ p.a. SI in the same time. What is the value of $\displaystyle r$ ?

Options

\displaystyle 10\%

\displaystyle 8\%

\displaystyle 12\%

\displaystyle 6\%

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 8\%$

All Options:

A $\displaystyle 10\%$
B $\displaystyle 8\%$
C $\displaystyle 12\%$
D $\displaystyle 6\%$

Detailed Solution & Explanation

**Derivation of Rate of Simple Interest** Given: - Amount at

\displaystyle r\%

simple interest in

\displaystyle 3

years (

\displaystyle A_1

) =

\displaystyle \text{Rs. }15,748

- Amount at

\displaystyle (r+2)\%

simple interest in

\displaystyle 3

years (

\displaystyle A_2

) =

\displaystyle \text{Rs. }16,510

**Step 1: Express the difference in amounts** The difference in the two amounts is due to the additional simple interest earned from the increase in rate by

\displaystyle 2\%

\text{Additional Simple Interest} = A_2 - A_1 = 16510 - 15748 = \text{Rs. }762

**Step 2: Find the Principal (

\displaystyle P

) using the additional simple interest**

\text{Additional SI} = \frac{P \times \text{Additional Rate} \times t}{100}

762 = \frac{P \times 2 \times 3}{100}

762 = \frac{6P}{100}

6P = 76200 \implies P = \text{Rs. }12,700

**Step 3: Solve for the rate of interest (

\displaystyle r

)** Using the simple interest earned in the first case:

SI_1 = A_1 - P = 15748 - 12700 = \text{Rs. }3,048

SI_1 = \frac{P \times r \times t}{100}

3048 = \frac{12700 \times r \times 3}{100}

3048 = 381 r \implies r = \frac{3048}{381} = 8\% \text{ per annum}

Hence, **Option B** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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A certain sum amounts to 15,748\displaystyle 15,74815,748 in 3\displaystyle 33 years at simple interest at 1%\displaystyle 1\%1% p.a. The same sum amounts to 16,510\displaystyle 16,51016,510 at r+2%\displaystyle r+2\%r+2% p.a. SI in the same time. What is the value of r\displaystyle rr?