Multiple choice

An amount of Rs. 12,000 is deposited in bank P for a certain number of years at a simple interest rate of 7% per annum. On maturity, the total amount received is deposited in bank Q for another 10 years at a simple interest rate of 8% per annum. If the interests received from bank P and bank Q are in the ratio 35 : 68, then the investment period, in years, in bank P is

  1. 6

  2. 8

  3. 10

  4. 12

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest P = (12000 * 7 * T) / 100 = 840T. Amount P = 12000 + 840T. Interest Q = (Amount P * 8 * 10) / 100 = 0.8 * (12000 + 840T). Ratio = 840T / (0.8 * (12000 + 840T)) = 35/68. Solving for T gives 10.

AI explanation

Let the time period for the investment in bank P be T years. The interest from bank P is calculated using the simple interest formula as 12000 multiplied by 7 by T divided by 100, which equals 840T. The maturity amount from bank P is 12000 + 840T, and the interest earned from bank Q over 10 years at 8 percent is calculated as 10 percent of the maturity amount, since the rate of 8 percent multiplied by 10 years gives an 80 percent return, making the interest equal to 9600 plus 672T. Equating the ratio of the two interests to 35:68, we get 840T divided by (9600 + 672T) equals 35 divided by 68. Solving this equation, 57120T equals 336000 plus 23520T, which gives 33600T equals 336000 and T equals 10. The investment period in bank P is 10 years.

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