Mathematics for FinancePYQ Nov 19Question 1295 of 512
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A trust fund has invested 30,000\displaystyle 30,000 in two different types of bonds which pays 5%\displaystyle 5\% and 7%\displaystyle 7\% interest respectively. Determine how much amount is invested in second type of bond if trust obtains an annual total interest of 1600\displaystyle 1600.

Options

A5000\displaystyle 5000
B6000\displaystyle 6000
C7000\displaystyle 7000
D8000\displaystyle 8000
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Correct Answer

✅ Option a — 5000\displaystyle 5000

All Options:

  • A5000\displaystyle 5000
  • B6000\displaystyle 6000
  • C7000\displaystyle 7000
  • D8000\displaystyle 8000

Detailed Solution & Explanation

**Derivation of Invested Sum in Bond Type 2** Given: - Total trust fund = Rs. 30,000\displaystyle \text{Rs. }30,000 - Interest rate of first bond = 5%\displaystyle 5\% per annum - Interest rate of second bond = 7%\displaystyle 7\% per annum - Total annual interest received = Rs. 1,600\displaystyle \text{Rs. }1,600 **Step 1: Set up the variables** Let x\displaystyle x be the amount invested in the first bond (5%\displaystyle 5\%). Then, the amount invested in the second bond (7%\displaystyle 7\%) is (30,000−x)\displaystyle (30,000 - x). **Step 2: Set up the annual interest equation** 0.05x+0.07(30000−x)=16000.05 x + 0.07(30000 - x) = 1600 0.05x+2100−0.07x=16000.05 x + 2100 - 0.07 x = 1600 −0.02x=1600−2100-0.02 x = 1600 - 2100 −0.02x=−500-0.02 x = -500 x=5000.02=Rs. 25,000x = \frac{500}{0.02} = \text{Rs. }25,000 **Step 3: Solve for the amount invested in the second bond** Investment in Bond Type 2=30000−x=30000−25000=Rs. 5,000\text{Investment in Bond Type 2} = 30000 - x = 30000 - 25000 = \text{Rs. }5,000 Hence, **Option A** is the correct answer.

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