A man invested Rs.7500 for two years at the rate of X% p.a. on compound…

2022

A man invested Rs.7500 for two years at the rate of X% p.a. on compound interest and received total interest of Rs.3300. He invested Rs.4800 in scheme A, which offers simple interest for two years at the rate of _____% p.a., and he also invested Rs._______ in scheme B, which offers simple interest for two years at the rate of 12% p.a. Total interest received from scheme A is Rs._______ more than that from scheme B. Which of the following option/s is/are correct to fill the blank spaces?
(i) (X-5), 200X, 480
(ii) X, 4800, 360
(iii) 1.5X, 4000, 500

  1. A.

    None of these

  2. B.

    Only (i)

  3. C.

    Only (iii)

  4. D.

    Only (i) & (ii)

  5. E.

    Only (i) & (iii)

Show answer & explanation

Correct answer: B

Concept

Compound interest over 2 years on principal P at rate R% relates the amount to the principal by A = P(1 + R/100)², so the total interest is I = P[(1 + R/100)² − 1]. Simple interest for T years is SI = P×R×T/100. Here the same rate symbol X first appears in the compound-interest scheme, so X must be found from that scheme and then substituted into every blank that is written in terms of X.

Step 1 — Find X from the compound-interest scheme

  1. Principal = 7500, time = 2 years, total CI = 3300, so the amount = 7500 + 3300 = 10800.

  2. Apply A = P(1 + X/100)2: 7500(1 + X/100)2 = 10800.

  3. Divide: (1 + X/100)2 = 10800/7500 = 1.44.

  4. Take the square root: 1 + X/100 = 1.2, hence X/100 = 0.2 and X = 20.

Step 2 — Test each candidate set with X = 20

Scheme A always has principal 4800 for 2 years; scheme B has rate 12% for 2 years. A candidate set fixes A's rate, B's principal and the claimed excess of A's interest over B's interest.

  1. Set with A-rate (X−5) = 15%, B-principal 200X = 4000: SIA = 4800×15×2/100 = 1440; SIB = 4000×12×2/100 = 960; difference = 1440 − 960 = 480, which equals the stated 480. This set is consistent.

  2. Set with A-rate X = 20%, B-principal 4800: SIA = 4800×20×2/100 = 1920; SIB = 4800×12×2/100 = 1152; difference = 768, but the set states 360, so it is inconsistent.

  3. Set with A-rate 1.5X = 30%, B-principal 4000: SIA = 4800×30×2/100 = 2880; SIB = 960; difference = 1920, but the set states 500, so it is inconsistent.

Cross-check

Only the first set reproduces every stated number simultaneously (rate 15%, B-principal 4000, excess 480). The other two fail on the excess figure, so exactly one of the three sets fits, giving the answer “Only (i)”.

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