Mathematics for FinanceMTP Sep 24 Series IIQuestion 1432 of 512
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The Partners A & B together lent 3903\displaystyle 3903 at 4%\displaystyle 4\% p.a interest compounded annually. After a span of 7\displaystyle 7 years A gets the same amount as B gets after 9\displaystyle 9 years. The share of A is sum of 3903\displaystyle 3903 would have been

Options

A1875\displaystyle 1875
B2280\displaystyle 2280
C2028\displaystyle 2028
D2820\displaystyle 2820
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Correct Answer

✅ Option c — 2028\displaystyle 2028

All Options:

  • A1875\displaystyle 1875
  • B2280\displaystyle 2280
  • C2028\displaystyle 2028
  • D2820\displaystyle 2820

Detailed Solution & Explanation

Let the share of partner A be x\displaystyle x. Since the total amount lent is Rs. 3,903\displaystyle \text{Rs. }3,903, the share of partner B is 3,903−x\displaystyle 3,903 - x. Given parameters: * Rate of interest (r\displaystyle r) = 4%\displaystyle 4\% p.a. compounded annually, so i=0.04\displaystyle i = 0.04 * A's investment period = 7\displaystyle 7 years * B's investment period = 9\displaystyle 9 years According to the question, the amount A gets after 7\displaystyle 7 years is equal to the amount B gets after 9\displaystyle 9 years: x(1+i)7=(3,903−x)(1+i)9x(1+i)^7 = (3,903 - x)(1+i)^9 Dividing both sides by (1+i)7\displaystyle (1+i)^7: x=(3,903−x)(1+i)2x = (3,903 - x)(1+i)^2 x=(3,903−x)(1.04)2x = (3,903 - x)(1.04)^2 x=(3,903−x)(1.0816)x = (3,903 - x)(1.0816) x=4221.4848−1.0816xx = 4221.4848 - 1.0816x 2.0816x=4221.48482.0816x = 4221.4848 Solving for x\displaystyle x: x=4221.48482.0816=2,028x = \frac{4221.4848}{2.0816} = 2,028 Thus, the share of A in the sum of 3,903\displaystyle 3,903 is Rs. 2,028\displaystyle \text{Rs. }2,028. Hence, **Option C** is the correct answer.

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