A lent 6000 to B for 2 years and 1500 to C for 4 years and received total interest of 900 from both. The rate of interest when simple interest method calculated.

Option a: 5%. Solution: Derivation of Simple Interest Rate Given: - Sum 1 lent to B (P1) = text{Rs. }6,000 for t1 = 2 years - Sum 2 lent to C (P2) = text{Rs. }1,500 for t2 = 4 years - Total interest received from both B and C = text{Rs. }900 Step 1: Set up the Simple Interest equations text{Total Interest} = SIB + SIC 900 = 6000 x R x 2/100 + 1500 x R x 4/100 900 = 120 R + 60 R 900 = 180 R Step 2: Solve for R R = 900/180 = 5% text{ per annum} Hence, Option A is the correct answer.

A lent $6000$ to B for $2$ years and $1500$ to C for $4$ years and received total interest of $900$ from both. The rate of interest when simple interest method calculated.

The correct answer is Option a: $5\%$. **Derivation of Simple Interest Rate** Given: - Sum 1 lent to B ($P_1$) = $\text{Rs. }6,000$ for $t_1 = 2$ years - Sum 2 lent to C ($P_2$) = $\text{Rs. }1,500$ for $t_2 = 4$ years - Total interest received from both B and C = $\text{Rs. }900$ **Step 1: Set up the Simple Interest equations** $$\text{Total Interest} = SI_B + SI_C$$ $$900 = \frac{6000 \times R \times 2}{100} + \frac{1500 \times R \times 4}{100}$$ $$900 = 120 R + 60 R$$ $$900 = 180 R$$ **Step 2: Solve for $R$** $$R = \frac{900}{180} = 5\% \text{ per annum}$$ Hence, **Option A** is the correct answer.

Mathematics for FinanceMTP Nov 18Question 1272 of 512

All Questions

A lent $\displaystyle 6000$ to B for $\displaystyle 2$ years and $\displaystyle 1500$ to C for $\displaystyle 4$ years and received total interest of $\displaystyle 900$ from both. The rate of interest when simple interest method calculated.

Options

\displaystyle 5\%

\displaystyle 6\%

\displaystyle 7.5\%

\displaystyle 9\%

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Correct Answer

✅ Option a — $\displaystyle 5\%$

All Options:

A $\displaystyle 5\%$
B $\displaystyle 6\%$
C $\displaystyle 7.5\%$
D $\displaystyle 9\%$

Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Sum 1 lent to B (

\displaystyle P_1

) =

\displaystyle \text{Rs. }6,000

for

\displaystyle t_1 = 2

years - Sum 2 lent to C (

\displaystyle P_2

) =

\displaystyle \text{Rs. }1,500

for

\displaystyle t_2 = 4

years - Total interest received from both B and C =

\displaystyle \text{Rs. }900

**Step 1: Set up the Simple Interest equations**

\text{Total Interest} = SI_B + SI_C

900 = \frac{6000 \times R \times 2}{100} + \frac{1500 \times R \times 4}{100}

900 = 120 R + 60 R

900 = 180 R

**Step 2: Solve for

\displaystyle R

R = \frac{900}{180} = 5\% \text{ per annum}

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

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A lent 6000\displaystyle 60006000 to B for 2\displaystyle 22 years and 1500\displaystyle 15001500 to C for 4\displaystyle 44 years and received total interest of 900\displaystyle 900900 from both. The rate of interest when simple interest method calculated.