Mrs. Sudha lent 4,000 in such a way that some amount to Mr. A at 3% p.a. S.I. and rest amount to B at 5% p.a. S.I., the annual interest from both is 144. Find the amount lent to Mr. A.

Option a: 2,800. Solution: Derivation of Amount Lent to Mr. A Given: - Total sum lent = text{Rs. }4,000 - Rate of simple interest for Mr. A = 3% p.a. - Rate of simple interest for B = 5% p.a. - Total annual interest received = text{Rs. }144 Step 1: Set up the variables Let x be the amount lent to Mr. A. Then, the amount lent to B is (4000 - x). Step 2: Formulate and solve the annual interest equation 0.03 x + 0.05(4000 - x) = 144 0.03 x + 200 - 0.05 x = 144 -0.02 x = 144 - 200 -0.02 x = -56 x = 56/0.02 = text{Rs. }2,800 Hence, Option A is the correct answer.

Mrs. Sudha lent $4,000$ in such a way that some amount to Mr. A at $3\%$ p.a. S.I. and rest amount to B at $5\%$ p.a. S.I., the annual interest from both is $144$. Find the amount lent to Mr. A.

The correct answer is Option a: $2,800$. **Derivation of Amount Lent to Mr. A** Given: - Total sum lent = $\text{Rs. }4,000$ - Rate of simple interest for Mr. A = $3\%$ p.a. - Rate of simple interest for B = $5\%$ p.a. - Total annual interest received = $\text{Rs. }144$ **Step 1: Set up the variables** Let $x$ be the amount lent to Mr. A. Then, the amount lent to B is $(4000 - x)$. **Step 2: Formulate and solve the annual interest equation** $$0.03 x + 0.05(4000 - x) = 144$$ $$0.03 x + 200 - 0.05 x = 144$$ $$-0.02 x = 144 - 200$$ $$-0.02 x = -56$$ $$x = \frac{56}{0.02} = \text{Rs. }2,800$$ Hence, **Option A** is the correct answer.

Mathematics for FinanceMTP Jun 23 Series IIQuestion 1382 of 512

All Questions

Mrs. Sudha lent $\displaystyle 4,000$ in such a way that some amount to Mr. A at $\displaystyle 3\%$ p.a. S.I. and rest amount to B at $\displaystyle 5\%$ p.a. S.I., the annual interest from both is $\displaystyle 144$ . Find the amount lent to Mr. A.

Options

\displaystyle 2,800

\displaystyle 1,200

\displaystyle 2,500

DNone of these

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

Correct Answer

✅ Option a — $\displaystyle 2,800$

All Options:

A $\displaystyle 2,800$
B $\displaystyle 1,200$
C $\displaystyle 2,500$
DNone of these

Detailed Solution & Explanation

**Derivation of Amount Lent to Mr. A** Given: - Total sum lent =

\displaystyle \text{Rs. }4,000

- Rate of simple interest for Mr. A =

\displaystyle 3\%

p.a. - Rate of simple interest for B =

\displaystyle 5\%

p.a. - Total annual interest received =

\displaystyle \text{Rs. }144

**Step 1: Set up the variables** Let

\displaystyle x

be the amount lent to Mr. A. Then, the amount lent to B is

\displaystyle (4000 - x)

. **Step 2: Formulate and solve the annual interest equation**

0.03 x + 0.05(4000 - x) = 144

0.03 x + 200 - 0.05 x = 144

-0.02 x = 144 - 200

-0.02 x = -56

x = \frac{56}{0.02} = \text{Rs. }2,800

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

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Mrs. Sudha lent 4,000\displaystyle 4,0004,000 in such a way that some amount to Mr. A at 3%\displaystyle 3\%3% p.a. S.I. and rest amount to B at 5%\displaystyle 5\%5% p.a. S.I., the annual interest from both is 144\displaystyle 144144. Find the amount lent to Mr. A.