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Ghosh Babu's Bank Account Analysis

CAT 1991 Slot 1 · Data Interpretation & Logical Reasoning · Medium · Data Interpretation

This is a medium Data Interpretation & Logical Reasoning question set from the CAT 1991 Slot 1 paper. It tests Data Interpretation. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

Ghosh Babu deposited a certain sum of money in a bank in 1986. The bank calculated interest on the principal at 10 percent simple interest, and credited it to the account once a year.

  • After the 1st year, Ghosh Babu withdrew the entire interest and 20% of the initial amount.
  • After the 2nd year, he withdrew the interest and 50% of the remaining amount.
  • After the 3rd year, he withdrew the interest and 50% of the remaining amount.
  • Finally after the 4th year, Ghosh Babu closed the account and collected the entire balance of Rs. 11,000.

Question 1 of 2

The initial amount in rupees, deposited by Ghosh Babu was:

  1. A.

    25,000

  2. B.

    75,000

  3. C.

    50,000

  4. D.

    None of these

Answer

C

Explanation

Let initial principal = PP.

  • Year 1 end: Balance before withdrawal =P+0.1P= P + 0.1P. Withdraws 0.1P0.1P interest + 0.2P0.2P principal. Remaining principal = 0.8P0.8P.
  • Year 2 end: Interest =0.1×0.8P=0.08P= 0.1 \times 0.8P = 0.08P. Withdraws interest + 50%50\% of 0.8P=0.4P0.8P = 0.4P. Remaining principal = 0.4P0.4P.
  • Year 3 end: Interest =0.1×0.4P=0.04P= 0.1 \times 0.4P = 0.04P. Withdraws interest + 50%50\% of 0.4P=0.2P0.4P = 0.2P. Remaining principal = 0.2P0.2P.
  • Year 4 end: Interest =0.1×0.2P=0.02P= 0.1 \times 0.2P = 0.02P. Total balance collected = Principal (0.2P0.2P) + Interest (0.02P0.02P) = 0.22P0.22P. Given 0.22P=11,000  ⟹  P=50,0000.22P = 11,000 \implies P = 50,000.

Question 2 of 2

The total interest, in rupees, collected by Ghosh Babu was:

  1. A.

    12,000

  2. B.

    20,000

  3. C.

    4,000

  4. D.

    11,000

Answer

A

Explanation

Total interest withdrawn across 4 years:

  • Year 1 interest: 0.10P=5,0000.10 P = 5,000
  • Year 2 interest: 0.08P=4,0000.08 P = 4,000
  • Year 3 interest: 0.04P=2,0000.04 P = 2,000
  • Year 4 interest: 0.02P=1,0000.02 P = 1,000 Total interest = 5,000+4,000+2,000+1,000=12,0005,000 + 4,000 + 2,000 + 1,000 = 12,000 rupees.

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