Mathematics for FinanceMTP Apr 21Question 1321 of 512
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Two equal sums were lent out at 7%\displaystyle 7\% and 5%\displaystyle 5\% simple interest respectively. The interest earned on the two loans adds up to 960\displaystyle 960 for four years. Find the total sum lent out.

Options

A4000\displaystyle 4000
B3000\displaystyle 3000
C5000\displaystyle 5000
D6000\displaystyle 6000
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Correct Answer

✅ Option a — 4000\displaystyle 4000

All Options:

  • A4000\displaystyle 4000
  • B3000\displaystyle 3000
  • C5000\displaystyle 5000
  • D6000\displaystyle 6000

Detailed Solution & Explanation

**Derivation of Total Sum Lent Out** Given: - Two equal sums P\displaystyle P are lent out. - Rate for first sum (r1\displaystyle r_1) = 7%\displaystyle 7\% p.a. - Rate for second sum (r2\displaystyle r_2) = 5%\displaystyle 5\% p.a. - Time (t\displaystyle t) = 4\displaystyle 4 years - Sum of interests earned = Rs. 960\displaystyle \text{Rs. }960 **Step 1: Express total interest in terms of P\displaystyle P** Total Interest=SI1+SI2\text{Total Interest} = SI_1 + SI_2 960=P×7×4100+P×5×4100960 = \frac{P \times 7 \times 4}{100} + \frac{P \times 5 \times 4}{100} 960=28P100+20P100960 = \frac{28 P}{100} + \frac{20 P}{100} 960=48P100960 = \frac{48 P}{100} 960=0.48P960 = 0.48 P **Step 2: Solve for P\displaystyle P** P=9600.48=Rs. 2,000P = \frac{960}{0.48} = \text{Rs. }2,000 **Step 3: Calculate the total sum lent out** Total Sum Lent=P+P=2000+2000=Rs. 4,000\text{Total Sum Lent} = P + P = 2000 + 2000 = \text{Rs. }4,000 Hence, **Option A** is the correct answer.

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