Mathematics for FinancePYQ Jan 21Question 1215 of 512
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Two equal amounts of money are deposited in two banks each at 15%\displaystyle 15\% p.a. 3.5\displaystyle 3.5 year in the bank and for 5\displaystyle 5 years in the other. The difference between the interest amount from the bank in 144\displaystyle 144. Find the sum

Options

A620\displaystyle 620
B640\displaystyle 640
C820\displaystyle 820
D840\displaystyle 840
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Correct Answer

✅ Option b — 640\displaystyle 640

All Options:

  • A620\displaystyle 620
  • B640\displaystyle 640
  • C820\displaystyle 820
  • D840\displaystyle 840

Detailed Solution & Explanation

**Derivation of Principal Amount from Difference in Interest** Given: - Equal amounts (P\displaystyle P) deposited in two banks. - Rate of Interest (r\displaystyle r) = 15%\displaystyle 15\% per annum simple interest. - Time periods: t1=3.5\displaystyle t_1 = 3.5 years and t2=5\displaystyle t_2 = 5 years. - Difference between the interests earned (SI2−SI1\displaystyle SI_2 - SI_1) = Rs. 144\displaystyle \text{Rs. }144 **Step 1: Set up the Simple Interest difference equation** SI2−SI1=P×r×t2100−P×r×t1100SI_2 - SI_1 = \frac{P \times r \times t_2}{100} - \frac{P \times r \times t_1}{100} 144=P×15×(t2−t1)100144 = \frac{P \times 15 \times (t_2 - t_1)}{100} 144=P×15×(5−3.5)100144 = \frac{P \times 15 \times (5 - 3.5)}{100} 144=P×15×1.5100144 = \frac{P \times 15 \times 1.5}{100} 144=0.225P144 = 0.225 P **Step 2: Solve for Principal (P\displaystyle P)** P=1440.225=Rs. 640P = \frac{144}{0.225} = \text{Rs. }640 Hence, **Option B** is the correct answer.

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